In the Honeybee Inn isn't Cait Sith in a room with Reeve's parents? They both talk about their son working for Shinra so it makes sense. I think the Cait Sith you see there must be a mini Cait as it looks tiny. Perhaps a little prototype for the real thing.

I think the scene is there just to give you a hint that Cait's a no-good Shinra spy.