Must be an iPad thing. I have two Android tablets, both with a Tivo remote app present. Both work fine. I have not tried using both simultaneously, sending competing commands. Both had to be loaded with the Tivo's MAK.
I only have one Tivo so I can't test, but it looks like the Android app could switch between multiple Tivos, too.
I only have one Tivo so I can't test, but it looks like the Android app could switch between multiple Tivos, too.