Eh, I think the show does a really good job explaining Emma's motivations throughout, chief among them being that she's not going to let anything stop her from doing what she wants even if it kills her. I don't know how much of it you've watched cause that is in season 1, but her CF crops up in a lot of realistic ways throughout the whole of the show. Maybe that hike wouldn't have been possible but it wasn't a particularly large suspension of disbelief for me.
season 3 Emma spoilersI thought it was much harder to believe that any hospital would move someone up a donors list for a mere $20,000. Like, that's some serious medical ethics being broken for not that much money