Green Day? I've never seen them perform as a trio, but always with another guitarist hiding in the shadows. And as much as I love Hot Tuna, they're really a duo with augmentation from various other players so they range from just Jack and Jorma to being a five-peice at times.
And I have trouble with "power trios" that relegate the bass and drums to regurgitating the same static patterns over and over so the guitarist can masturbate seemingly endlessly. As great as Tommy Shannon and Chris Layton are, I don't consider SRV/Double Trouble a great rock trio, and I think Z Z Top falls into the same place. But that's why Cream and JHE are at the head of this list. Those were active three-piece bands where everyone was actively communicating, listening, feeding off of and feeding back to each of the others- totally interactive at all times (at least on the good nights). The danger of that of course is that it can fall into simultaneous soloing instead of challenging musical conversations.
I love that they put The Police in there, because that trio embraced the sparseness that bass/drums/guitar has at its inherent core. Instead of trying to fill everything up, they chose to leave those spaces wide open and use that as part of the music. Like T. R. Kelly said, "without space, music is just noise piling up on itself".
I don't know nor care enough about Rush, Muse, nor Primus to have anything intelligent to comment on their places in the list.
MY list would be...
10. Emerson, Lake, and Palmer (but Gibson wouldn't have put them there 'cause they don't have a guitarist!)
9. Rory Gallagher's bands (especially Gerry McAvoy and Rod de'Ath, the band on "Tatoo")
8.Jeff Beck with Vinnie Colaiuta and Tal Wilkenfeld
7. Robben Ford with Roscoe Beck and Vinnie Colaiuta
6. BLT (Jack Bruce, Bill Lordan, Robin Trower)
5. Mountain
4. The Police
3. The James Gang
2. The Jimi Hendrix Experience
1. Cream
