I've been told by my Honda mechanic and, of course, tire dealers, that on AWD vehicles like my Honda CRV AWD, you can not replace just one tire, but have to replace all of them unless the tread is within a certain depth. I also thought I read it in my Honda CRV repair manual, but all I have found in that bohemous trug are comments on not towing with two wheels only and jacking up the whole car so all the wheels can turn while working on the drivetrain.
Tire replacement on AWD - one or all? on 1999 Honda CR-V
On AWD vehicles, you can get away with a slight variation in tire tread depth. It's best to have matching tire types and sizes but a little difference in wear depth is tolerable.
to add to bobs answer, the different rotation speeds plays badly with the transfer case. it could cause internal damage to the case assembly if the tires are different depths.
FALSE: The difference in tire circumference caused by under-inflation of one tire is significantly greater than the differerence in a 10K and 35k worn tire... this 'change all 4 tires' is a marketing scheme and has no basis in science.