Having worked on/contributed to one of the comms packages for Air Force One, immediately after 9/11; for the record, there's a specific reason for paint on the 25A's and 25B's.
If your sister paid for her cat to fly, no problem. For 17 years my cat traveled both in the cabin and below (temperature permitting), domestic and long-haul international. Yep, 'ESA' freebies are a scam.