HUGE Phish fan here, been to close 100 shows but no way Fishman is in this kind of elite elite talk of drummers and I LOVE Jon Fishman...don't know much Tool so I cannot comment on Carey but I'd say Beauford is in the conversation and Sexton is not.
I've thought on this for a couple of days and for me its...
(1) Peart
(2) Bonham
(3) Bozzio
Fishman is a master in every sense of the word and is definitely amongst the elite of all time, and I say this as a drummer and drum instructor who has been playing for 22 years and teaching for over 10. He is a rudimental master and, like Carter Beauford, Danny Carey, and Chad Sexton, incorporates those rudiments and rhythms into his music. Those guys don't just play simple, basic beats over and over again. They are rhythmic geniuses who have mastered independence with both their hands and feet and they also have insane chops. They aren't just drummers; they are truly percussionists who understand what goes where and know how to incorporate chimes, temple blocks, jam blocks, gongs, etc into their playing. Awesome that you're a Phish fan! I love them but have never had the chance to see a concert. I've seen DMB 16 times and Carter has been my major influence since I was in middle school, but I have to respectfully disagree with you about Fishman. The dude can flat out play, and few others in the industry have mastered the art like he has, other than the guys that both you and I have mentioned.