SHIELD may be taking the view that, since they're espionage, their job is to keep people alive and get them through the current crisis, then--hopefully-hook them up with resources later. That might be why they sent Phil to Tony, so he could have a handler, since he needed that kind of personal help. It's not an uncommon view in first responders, and it often fails at the second part, like I imagine SHIELD does.

And yes, Bruce-and-Hulk seem like Bruce has been reading up on medical ethics from patients' POV and both of them are applying it in real time.