How to tell if a chip's heat sink can be grounded

In general, the thermal pad is grounded. Your interpretation of the missing information is correct.
Apparently, you are supposed to read some application note that is not referenced from the datasheet.

Yes it is really unclear on the spec sheet and the app-note does not help either.

Without more information or calling the manufacturer you would need the part in hand to test it.

If you plan on going ahead before you get the parts, you really don't want to leave a big copper pad like that floating. Which is why it may be grounded on that schematic, but not shown on the part info, it may not be internally connected at all but just a thermal pad.

If in doubt it would be better to route it out through a small cap or resistor you can short out later when you have the parts in hand.

Adding the extra pin to the symbol will also make life a lot less confusing for the PCB designer later too.