The op's assertion that autonomous vehicles rely "heavily" on GPS data is false. The problem he presents will not occur.
This won't happen because the computer does not use GPS to determine drivability and will not drive the car into underivable conditions, and the computer will have selected a drivable route to begin with because it can select from routes that have previously been driven. If a route that was previously drivable becomes underivable due to local conditions, the car simply re-routes.
Neither the apparent drivability of mapping data, nor position within that data as computed by GPS effect the car's ability to travel autonomously from point A to point B.
It's certainly not reading signs. The system doesn't currently have that capability. It's a combination of GPS (to know where it is) and maps (to know how to go from where it is to the destination).
I 100% agree with you that the problems presented in the original comment wouldn't be an issue. The cars will use local data to determine whether a surface is drivable. They won't drive into sand or deep snow just because the navigation says that they should.
But that's not the same as your statement that they won't use GPS at all. And your statement that Tesla currently doesn't use GPS in their systems is plainly wrong.
I did not say Tesla's don't use GPS, they do. I said "It is unlikely that fully autonomous cars will use any GPS at all". My argument is not that you can't get google maps in your car, my argument is that the autonomous cars of the "Utopian future" will not need google maps to function, much less leave you stranded in an incorrectly mapped location.
Since you mentioned Tesla’s current systems, note that this is how they work now. Lane keeping is entirely local, but decisions about which lane to be in or which exit to take to reach your destination are done with your GPS position.