A bromance happens when two guys have hung around each other/worked together/ played together for long enough to actually care what happens to the other for more than just a feeling of 'obligation'.
Greer would save Scott's life and vice versa, but not because it's "them", rather just because it's their 'job'. That's not a bromance, that's a co-worker.
John and Rodney had a bromace. No two ways around it. When one was in severe trauma the other would always be there even if it was awkward as hell. Same with Ronon.
Slash? I could see where it's coming from ,but TBH that's not John. Rodney maybe but John is quite straight and while he seems to have no issues with gays, he clearly isn't given that he's canonically attracted to women, not men (Just look at how he peeks down Larrin's shirt when she leans towards him!
)
Will that stop slashers? Nah. I draw the line at sharing bodily fluids, but a bromance is always fun.
I always find myself thinking of American Dad when it comes to whether it's 'slash' or not. When Stan tried to force himself to be gay, he just couldn't get excited. I see the same with John.
Friendships like that take time. It's natural for people to tease each other and such, and over the course they find out about each other, yadda yadda, next thing you know it's Rodney with a parasite in his brain and of all people he's calling out for John.
Here's a question, would John in the same situation call for Rodney? I don't think so. I think he would have tried to endure and stay quiet, but maybe he'd mutter something about Nancy.