can the iphone keep a key fob from working

I guess it's always possible since key fobs are in an unlicensed frequency. There are often warnings that devices can't cause dangerous interference (i.e. can't mess with pacemakers or the like), but that any device must accept any interference.

But yeah it could happen, although it's impossible to know without someone with a frequency spectrum tool.

https://www.maximintegrated.com/en/design/technical-documents/app-notes/3/3945.html

Abstract: In a remote keyless entry (RKE) system, a car is unlocked from a distance by a radio code sent from a key fob to a receiver in the car. RKE systems usually operate at frequencies in the unlicensed ISM band that includes 315MHz and 433.92MHz. With the advent of remote starting features and two-way RKE with verification, designers want to increase the usable range of these short-range devices. Replacing SAW resonator transmitters with high-frequency, tolerance phase-locked-loop transmitters allows receivers with narrower bandwidth to be used.

My daughter always keeps her iPhone and her key fob in her purse, and she never had a problem.

To make sure, ask your car manufacturer about that.

Regards

Giulio