With a client, it's about the software you're developing, with a interviewer, it's about software architecture or coding principles.

In your example about HTML -> CSS I think you missed the point. It wasn't so much to check that you have something memorized, but to check your familiarity with the subject. Everyone sits with a browser while they code - I don't think that's a unique workflow. The thing is, if you've done this HTML -> CSS conversion a hundred times before, you wouldn't need to look it up. They're trying to gauge your experience level and if you've done this stuff hundreds of times before. I bet even a highschool student could find that with Google.

EDIT: I think a more relatable example would be if the interview gave you a simple geometrical problem and you were upset you can't look up the Pythagorean theorem. You're not being tested on your ability to memorize the Pythagorean theorem per se - it's just that everyone is expected to know the Pythagorean theorem b/c it's so fundamental to the sciences. Super simple problem with no google are testing if you have domain familiarity and experience and are a metric of whether you will hit the ground running or not. They're not gauging you problem solving ability, or your ability to memorize crap.