Natasha's a spy, why would she be involved in treating Peter? Probably there in case Bruce hulks out -- so really not doing her job.

Bruce has PhDs in nuclear physics, biochemistry, radiophysics, engineering, robotics, computer science, and mathematics, but the MCU Bruce does also have an MD (Medical Doctorate), so he'd be vaguely qualified.

But you'd think they would have called Doctor Strange. He was a practicing surgeon with an MD and a PhD in neurobiology. Plus, if you're suffering from priapism -- he could literally invoke the Greek God Priapus to fix it. :-)

Base +11, GG141 -4, Romi the Byzantine +8