At work, I was told to check out a flat tire on one of our fleet trucks
When I dismounted the tire, guess what I found inside?
A file, complete with part of the handle . . . !
The puncture wound didn't seem big enough to explain the file, but it was in there
Naturally, I discarded the tire and mounted a new one
So yeah, given that I saw a file inside a tire, I think it's entirely possible for a key to puncture a tire