Is the thing where English teachers insist upon "may" instead of "can" where appropriate just a meme or does it actually happen a lot?

We Finns have it in reverse. Informal language maintains almost exclusively separate verbs for being able to, and being allowed to (voida/kyetä/pystyä and saada, respectively) but in many formal contexts, eg. in the army, the word "voida" is used for both and it's enforced as a part of army communication.

@kviiri It's a shibboleth for "proper education."