Hey, Chepie, I'd be asking your GP for clarification of that comment!! Your tube does not 'move across' to collect another egg. At all. Your fallopian tube is connected to your ovary and it does not disconnect at any stage nor does it reconnect to your other ovary in the absence of a fallopian tube. Ever.

I'm sorry if I sound blunt, but... no.
I'm with Nickle - your tube can't physically move from one side to the other.

When you ovulate from the ovary that has no tube, the egg is reabsorbed into the body.