I'm a college professor. I try to teach my students enough that they know what to Google, and that they can understand and use the result. I can't teach nearly everything they might need in the future, but I can give them the foundation.
“He aggressively encourages the use of search engines”
Because every time they would ask me a question I would ask them if they tried to Google it first.
I'm not sure why people think software development (and computers in general) is somehow different. We don't know everything. We basically can't.
What we (and all other professions) have is knowledge on how to apply new information to what we already know.
So yes, you're right. You have to teach the basics, how to put them together and how to add new pieces once you inevitably hit something you don't know.
If the physician you were at felt unable to make the right call, he could have referred you to or consulted with someone who could. An 'irritated look' might instead be a flurry of such treatment paths going through their mind.
'Can I figure this out on my own? Should I consult? Should I refer out? Should I just check UpToDate? What does the latest literature I read say to do? What was done for the last patient who had this? Has the literature changed since then? What is the hospital policy on this (if any?)? What did my microbiology class say to do for this? What do the boards think is right to do in this instance?'