During a riot, what do prisoners have to reach to get guns?

I'm reasonably confident that I've now found the answer in the original alpha release video:

Proceeding frame by frame (by mashing the space key) from 12.01, you can just about make out that the prisoners magically have guns in their hands as soon as they hit the first armoury tile. This would mean that my original suggestion wouldn't be secure.

I can't be entirely sure as things may have changed in alpha 18, however I can say that this is the answer in the interim before I work out a way to cause a test riot.

In addition to your own answer I would say it does not matter whether they have to touch the gun rack or just get in to the room, as they are going to be armed by the time your guards get there.

Essentially by having heavier doors, and or more of them, between your prisoners and the armoury room you are giving guards more time to suppress rioting prisoners before they get to the guns.

If you are really paranoid about your prisoners getting in I'd put an armed guard on patrol outside the exclusion corridor; if you put them inside they will just unlock the door to get to the rioting prisoners and therefore negate the security of having another door.

You asked if your design is safe; I'd avoid having an armoury connected directly to a cell bock (the door to the right in your picture) as this is providing the most direct route to the guns for a large number of prisoners. Where possible I put the armoury as far from the cells as possible.

Edit 02/02/2016:

I now build the Armoury outside the main prison, usually just over the road. The room only has to fit one gun rack, a table and as many lockers as you need guards so a narrow, long room does the job.

Rioting/escaping prisoners will run for freedom if they manage to get out of the prison and not towards the Armoury, negating the problem of prisoners arming themselves.

Although it's still wise to use a strong door.