Can Apps spy on one another?

I drive for both Lyft and Uber. There's a conventional wisdom among drivers that I have met that each company knows when you have the other's app open on your phone (with a variety of consequences resulting.)
Does the iOS API allow such spying?

Thanks,
Rob

I'd be EXTREMELY surprised if this was the case. There's obviously integration between social media apps but I can't see the uber/lyft example being true

Each app on an iOS device is isolated from other apps and the OS. There is no way for one to be aware of the other or interfere with the other.

That "conventional wisdom" sounds more like paranoia..

Each app is sandboxed from one another as long as the device is not jail broken.