The skill menu is just how you said; if you don't click the tick before exiting the menu, it takes it as you cancelled your actions. The tick button is like "accept" I guess, and the cross is "exit". I've done this a couple of times and had to re-level up.
I just noticed this: you have to confirm the change. I was relieved, too, to discover that removing all 5 points spent on fire missiles only cost 3333 coins (Act I).
