It is a similar problem, however: https://en.wikipedia.org/wiki/Birthday_problem#Same_birthday...
If I can generate a key that hashes to the same value as your key, I can convince anyone I am you. If I can generate a second collision for a third party's key, I can convince you you are talking to that third party, as well. Generating hash collisions is, as I understand it, pretty well modelled with the birthday paradox (and variations like the one I linked). Physical proximity seems entirely unrelated.