How can a Point NOT be Within or Touch but still Intersect a polygon?

ST_Within(A,B) tells you whether "A is within B". Is the polygon within the point? Nope. ST_Contains(A, B) tells you whether "A contains B" and it is.

SELECT ST_Within(geom,pt), ST_Contains(geom,pt), ST_Touches(geom,pt), ST_Intersects(geom,pt)
FROM ( VALUES
    (
    ST_SetSRID( ST_GeometryFromText($$MULTIPOLYGON(((-88.466933 42.139013,-88.464586 42.139034,-88.463821 42.13901,-88.463811 42.138813,-88.463815 42.138705,-88.46382 42.138572,-88.463849 42.138468,-88.463886 42.138398,-88.464044 42.138452,-88.464239 42.138464,-88.464616 42.138472,-88.464961 42.138468,-88.465318 42.13846,-88.465558 42.138464,-88.465695 42.138443,-88.465824 42.138402,-88.465969 42.138319,-88.466048 42.138248,-88.466106 42.138161,-88.466135 42.138057,-88.466148 42.1379,-88.466149 42.137731,-88.466143 42.137406,-88.466143 42.137086,-88.466131 42.136945,-88.466098 42.13685,-88.466027 42.136746,-88.46596 42.136677,-88.465799 42.136609,-88.465571 42.136559,-88.465359 42.136534,-88.465167 42.136547,-88.464221 42.136559,-88.464216 42.136248,-88.464199 42.13609,-88.464179 42.135999,-88.46412 42.13587,-88.464046 42.135779,-88.463847 42.135597,-88.463531 42.135373,-88.463341 42.135252,-88.46313 42.135068,-88.462915 42.134957,-88.462601 42.134865,-88.462337 42.134822,-88.461619 42.134822,-88.460882 42.134828,-88.46044 42.134834,-88.460047 42.13484,-88.460053 42.135105,-88.460047 42.135381,-88.460034 42.135461,-88.459985 42.135559,-88.459905 42.135651,-88.459825 42.135756,-88.459752 42.135848,-88.459703 42.135934,-88.459684 42.136001,-88.45966 42.136118,-88.459654 42.136259,-88.459647 42.136836,-88.459107 42.136824,-88.458855 42.136818,-88.45864 42.136855,-88.458407 42.136978,-88.458315 42.137082,-88.458272 42.13718,-88.458247 42.137291,-88.458235 42.137408,-88.458241 42.137537,-88.458247 42.137647,-88.458253 42.138421,-88.458235 42.139017,-88.457615 42.139023,-88.457197 42.139029,-88.456607 42.139066,-88.455926 42.139146,-88.455133 42.139256,-88.45474 42.139313,-88.454709 42.139196,-88.454716 42.13907,-88.454683 42.138859,-88.454646 42.138353,-88.454669 42.138226,-88.454628 42.137907,-88.454616 42.137669,-88.454626 42.137153,-88.454611 42.137072,-88.454576 42.136978,-88.454512 42.136892,-88.454395 42.136793,-88.454355 42.136747,-88.454314 42.13659,-88.454306 42.136383,-88.454232 42.136322,-88.454175 42.136293,-88.454087 42.136261,-88.453929 42.136244,-88.453854 42.136242,-88.45377 42.136248,-88.453595 42.136284,-88.453339 42.136363,-88.453245 42.136397,-88.453161 42.136445,-88.453091 42.136465,-88.452984 42.136463,-88.452758 42.136445,-88.452403 42.136441,-88.452284 42.13642,-88.452172 42.136401,-88.451882 42.136359,-88.451677 42.136347,-88.45101 42.136297,-88.450681 42.136267,-88.450621 42.136253,-88.450506 42.136233,-88.450417 42.136208,-88.450304 42.136162,-88.450194 42.13611,-88.45004 42.13605,-88.449814 42.135954,-88.449742 42.135934,-88.44962 42.135916,-88.449449 42.135913,-88.448948 42.135919,-88.448035 42.135911,-88.447642 42.135913,-88.447494 42.135908,-88.4472 42.135908,-88.447133 42.135897,-88.446934 42.13583,-88.446806 42.135794,-88.446619 42.135764,-88.44654 42.135733,-88.446374 42.135693,-88.446295 42.135691,-88.446062 42.135732,-88.445985 42.135752,-88.445877 42.135766,-88.445808 42.135768,-88.445736 42.135761,-88.445664 42.135738,-88.445495 42.135652,-88.445404 42.135599,-88.44532 42.135556,-88.445258 42.135506,-88.445209 42.135449,-88.445154 42.135363,-88.44512 42.135297,-88.445108 42.135274,-88.445041 42.135094,-88.444995 42.135001,-88.444959 42.134915,-88.444908 42.134837,-88.444846 42.134763,-88.444795 42.134717,-88.444739 42.134677,-88.444663 42.134636,-88.444579 42.134617,-88.444485 42.134605,-88.444233 42.134608,-88.444145 42.134617,-88.444044 42.134637,-88.443934 42.134652,-88.44379 42.134686,-88.443725 42.134696,-88.443549 42.134682,-88.44342 42.134663,-88.44335 42.134643,-88.443252 42.134599,-88.443115 42.134602,-88.442976 42.13462,-88.442873 42.134642,-88.442774 42.134674,-88.442618 42.134767,-88.442551 42.134783,-88.442501 42.134819,-88.442441 42.134853,-88.442345 42.134882,-88.44228 42.13488,-88.44221 42.134857,-88.442107 42.134807,-88.442023 42.134755,-88.441961 42.134695,-88.441917 42.134632,-88.44191 42.134553,-88.441919 42.134482,-88.441996 42.134302,-88.442027 42.134205,-88.442039 42.134084,-88.442036 42.134019,-88.442012 42.133923,-88.441966 42.133862,-88.44189 42.13383,-88.441743 42.133808,-88.441565 42.133793,-88.441433 42.133798,-88.441253 42.133811,-88.440949 42.13385,-88.440761 42.133852,-88.440644 42.133824,-88.440548 42.133781,-88.440298 42.133605,-88.440192 42.13351,-88.440153 42.133451,-88.440125 42.133391,-88.439999 42.13319,-88.439932 42.133128,-88.43987 42.133078,-88.439805 42.133033,-88.439663 42.132971,-88.439317 42.132844,-88.439019 42.132728,-88.438784 42.132647,-88.438695 42.132611,-88.438599 42.132588,-88.438405 42.132574,-88.438345 42.132561,-88.438273 42.132574,-88.438234 42.132576,-88.438001 42.132417,-88.437931 42.132361,-88.43785 42.132306,-88.437624 42.132201,-88.437463 42.132137,-88.437208 42.132053,-88.437129 42.132019,-88.436992 42.132,-88.436788 42.131979,-88.436678 42.131963,-88.436565 42.131939,-88.436488 42.131918,-88.436205 42.131804,-88.436123 42.131761,-88.436032 42.131731,-88.435981 42.131695,-88.435953 42.131665,-88.435936 42.131624,-88.435888 42.131579,-88.435626 42.131274,-88.435578 42.131238,-88.435522 42.131165,-88.435409 42.131043,-88.435294 42.130892,-88.435229 42.13084,-88.43502 42.130604,-88.434892 42.130467,-88.43439 42.129908,-88.434291 42.129803,-88.434111 42.129599,-88.434051 42.129544,-88.434007 42.129515,-88.4337 42.129405,-88.433628 42.129373,-88.433554 42.129314,-88.433501 42.129257,-88.433481 42.129203,-88.433475 42.129,-88.434945 42.128994,-88.435401 42.128955,-88.436779 42.128706,-88.437438 42.128631,-88.437986 42.128635,-88.438514 42.128698,-88.439106 42.128842,-88.441903 42.129725,-88.442869 42.130081,-88.444453 42.130597,-88.447242 42.131469,-88.447807 42.131653,-88.448286 42.131788,-88.448679 42.131886,-88.449035 42.131948,-88.449502 42.131977,-88.451438 42.132031,-88.452216 42.132022,-88.453027 42.132095,-88.453641 42.132193,-88.454022 42.132267,-88.455004 42.132451,-88.455582 42.132587,-88.456073 42.132771,-88.456687 42.133029,-88.457178 42.133274,-88.457433 42.133409,-88.458097 42.133717,-88.458735 42.134017,-88.458987 42.134122,-88.459504 42.134245,-88.459832 42.134282,-88.460495 42.134263,-88.461281 42.134263,-88.461905 42.134249,-88.462648 42.134259,-88.462991 42.134306,-88.463362 42.134392,-88.463604 42.134506,-88.463705 42.134554,-88.463991 42.134706,-88.464239 42.134897,-88.464391 42.135068,-88.46467 42.135368,-88.464905 42.135602,-88.465077 42.135754,-88.465286 42.135916,-88.465429 42.135983,-88.465667 42.136068,-88.465924 42.136106,-88.466362 42.136116,-88.466905 42.136087,-88.466935 42.137029,-88.466933 42.139013),(-88.458229 42.134374,-88.458161 42.134318,-88.457492 42.133962,-88.456546 42.133502,-88.456091 42.133293,-88.455809 42.133188,-88.455551 42.133133,-88.455471 42.133102,-88.455385 42.133158,-88.45533 42.133244,-88.455299 42.13336,-88.455275 42.133471,-88.455282 42.133657,-88.455274 42.133965,-88.455279 42.133988,-88.455294 42.134017,-88.455319 42.134042,-88.45533 42.13405,-88.455351 42.134062,-88.455388 42.134075,-88.455429 42.134081,-88.45546 42.13408,-88.455658 42.134071,-88.455717 42.13407,-88.455796 42.134076,-88.455874 42.134088,-88.455948 42.134108,-88.45602 42.134134,-88.456046 42.134146,-88.456482 42.134355,-88.457315 42.134739,-88.457836 42.135006,-88.457946 42.134877,-88.458112 42.134687,-88.458204 42.134552,-88.458247 42.134447,-88.458229 42.134374),(-88.452273 42.135697,-88.452285 42.135431,-88.452274 42.135336,-88.452194 42.134994,-88.452165 42.134926,-88.452102 42.134856,-88.452036 42.134814,-88.451952 42.134783,-88.451842 42.134768,-88.450207 42.134731,-88.450045 42.134734,-88.449883 42.134753,-88.449809 42.134767,-88.449989 42.135232,-88.450033 42.13532,-88.450071 42.135375,-88.450125 42.135435,-88.450188 42.135489,-88.450274 42.135547,-88.450379 42.1356,-88.450498 42.135641,-88.450645 42.13567,-88.451787 42.135817,-88.45195 42.135827,-88.452057 42.135822,-88.452288 42.13579,-88.452273 42.135697)))$$), 4326 ),
    ST_GeometryFromText('POINT(-88.450000 42.135254)',4326)
    )
) AS t(geom, pt);

Here's the results as seen on my computer:

 st_within | st_contains | st_touches | st_intersects 
-----------+-------------+------------+---------------
 f         | t           | f          | t