Speaking of Physics - the properties of a game's physics engine have the properties of a Riemann sum where n=fps. so the higher your FPS the more accurate your physics simulation, even if your monitor cannot discretely display all those frames.
[note: only applies in games where physics ticks/sec are tied to framerate... which is almost all games]
Actually all decent FPS engines have geometry/physics engines quite distinct from the graphics-pipeline!
The geometry/physics engines work on body bounding-boxes and their respective velocity-vectors describing their trajectories, and they try to solve the intersection-problem among all bodies with regard to time, by responding with a timestamp - the collision-timestamp - to questions like this:
"When is body A going to hit body B?"
And on that collision-timestamp an event is scheduled, for the game-logic to kick-in, to calculate the new body-trajectories, or deaths, new body births, sarpnels, whatever.
The physics/geometry usually runs on the game-server *simultanesous* with the clients to avoid sending back-and-forth excessive info into the network. The server is only authoritative for the game-logic decisions. Yet the client runs additionally the graphics-pipeline which uses the next-frame's timestamp to calculate the body-positions on the 3D space.
But sometimes there is a slight delay between the collision-timestamp and the response from the server about what to do next (the game-logic's decision), that may allow a body to be drawn past its collisions point, and this is what make us think that FPS affects physics.
To sum it up, fps has nothing to do with physics, even if some times it seems that way.