Could Fluffy be doing "secret" binkies?
One of my rabbits binkies only in "secret". The humans can't know watch, or can only do so hidden away (think behind a curtain or a door). But, we know this because she does it fairly consistently, twice a day (early morning, and then again late morning), and she's been doing this for years and years. She goes on for about 30 minutes each time. You can also usually tell because she's a little out of breath afterwards.
Another one of my rabbits binkies only in tiny bursts, which aren't really noticeable unless you are paying attention. It happens usually when I bring out fresh hay, and he does a quick binky into the litter bin. It lasts about a second only. Otherwise, this guy has the most fun and writhing-around flopovers ever seen.