Quentin Quire: "Things are definetely gonna burn..." *image of an exploding planet*
That was good enough for Hank to want to destroy the phoenix in space. If the smartest Xmen thinks your plan is stupid without even a second thought, then your plan is probably stupid.
OK, points for you on Quentin. That COULD have been interpretted that way. I don't think that was what Quentin was seeing, though. I think the Phoenix destroying a planet was more to show US what the Phoenix was up to and what Quentin saw was what was shown in the panel where he DOES see the Phoenix... which is just a giant raging firebird in space.
But he could have seen the planet blowing up, maybe.
I still don't think Hank was influenced by any of that. He heard his Phoenix alarm go off, talked to Captain America, and leaped at the chance to stop the Phoenix from reaching Earth. Even if the Phoenix wasn't blowing up planets, this is exactly what the Avengers should be doing. The Phoenix as previously depicted isn't the sort of cosmic entity that blows up anything in it's path but that doesn't mean you want it on your planet.
When Hank and the rest of the Space Avengers get further in outer space, then they all know what the Phoenix Force is doing and at that point stopping the thing is the best idea ever. The undoubtedly relay that intel back to Earth, too, so the Avengers SHOULD know right about now, depending on how long it takes to send a message through space. I just don't think they knew when things started out and, other than Magneto, Cyclops and crew should have no idea. And Magneto? It doesn't seem like AvX VS. is actually happening in continuity. Go Marvel.