Is it possible to have bug in Webpage on same Bowers with same version but different OS(only desktop OS windows, mac,Ubuntu etc.)

One Webpage(W) running on browser(B) with version(V) and different desktop OS OSX(OS-O), Windows(OS-W), Ubuntu(OS-U) and etc.

W + B(V) + OS-O = OK
W + B(V) + OS-W = BUG or behave different from other OS
W + B(V) + OS-U = OK

I am not taking about browser bug. Here assume browser B don't have own internal bug.

give answer of this few questions.

1. above scenario possible or no
2. if yes then how and which situation
3. if no then why we still testing webpage for both OS with same browser