> There's no theoretical way for a hash map to work without storing the key - the reason for that is hash collisions in presence of which you do need to run equality comparison with stored keys otherwise you would overwrite data just because of hash clashes.

There's a ton of material in a Data Structures course. I'm sure the point about storing the key was mentioned at some point, but it's not the focus when talking about different hashing strategies etc. For people with a bunch of experience (e.g. I'd been writing Perl for years before this, so being able to iterate across a hash and get (k,v) pairs was obvious) it's a detail that is already there in your brain, but if the DS course is your first exposure to a hash map, it's a detail that can easily get lost in the huge forest of other brand new things to learn.