How thin/worn out can you allow road bike rims to get?
0.8mm is very thin and dangerous. The mechanic is right to tell you to replace the rim! Keep it only if you want to play with your life because it may fail in a catastrophic manner! More dangerous even on a front wheel.

Many rims have wear indicators, usually a couple of holes along the braking surfaces, that tell you that the rim is over the limit once one of the holes becomes invisible.