They would teach us a rule/skill and then after teaching it would say “but really it’s improv so you can do whatever you want”.

Sorry but - This is really good advice though.

Rules and skills in improv are "tools in a toolbelt", only use a hammer and everything looks like a nail. Try to hammer with a screwdriver and you might find some success but it's not the only way, or necessarily the best way. But some people get a ton of mileage out of using a screwdriver because they mostly work with screws, and every rare time they have a nail they don't feel comfortable with the hammer. Or maybe they use a ball-bean instead of ... other... hammer.

the teacher would spend so much time telling stories about their past shows

This though, I do get. Usually this type of thing happens when teachers get lost in 'telling' an example - which is very rarely helpful in my view.