I agree with most of what you're saying - except the "The Phoenix doesn't exactly have a track record of coming to Earth peacefully", because Rachel held the Phoenix for years with no real issue, and Jean/Phoenix clone of Jean (I'm not sure which one the editorial boneheads are claiming is canon now) held it together well until Mastermind started gaslighting her.
The X-Men's history, one that Logan would know having been present, is of Phoenix being dangerous elsewhere but never having been a direct threat to Earth, or at least not of its own volition.
I don't blame the Avengers for being careful, and they were right not to go off on a hunch, and Cyclops was a little too isolationist for his own good, but the way they went about it was all wrong. Put yourself in Scott's shoes:
Cyclops has just led mutantkind through probably inarguably the worst period it has ever experienced. The world threw everything at them, and they barely pulled through. Norman Osborn, America's top cop, tried to boss them around and attacked them, so they moved to their own island. Bastion and his ex-human bigot brigade then tried to destroy the island. And that doesn't mention the vampires, zombies and other assorted horrors.
So you pull through all of that, and your one guiding light is Hope. And now it seems that she will fulfill her duty. But wait - here come your allies. Are they here to help? (Were they ever?)
They want Hope. They're not asking for an explanation, they're not offering to work together, they're not appealing to your camaraderie after over a decade of fighting together.
No. "Give her to us." No if, whens, and buts. A direct order from a man who has no legal authority issuing them.
Imagine how it must feel to Scott, having lived for years hanging on to a thread, to see someone try to take it from him. A beloved human, the symbol of a nation that openly oppressed them and forced them out, trying to snuff out their last hope.
Wouldn't you fight back?