I guess since the I-class (like fish) have their eye forward when belly is on the ground, flipping them on their back would give them a feeling similar to standing on your head. But too bad for you. When Shigushigu wants to pet your belly, your damn belly is going to be petted for as long as she wants.
Ah... Excuse me Miss, could you not turn me upside down...
Errr... Are you listening...?