'becomes wet' and 'gets wet' are to my opinion similar. 'becomes' is even closer to the passive tense used here.
Does this sentence carry the "raining" meaning? Like "The hat gets rained on easily"?
Great, thanks, that's the type of explanation that I can count on you to give :) So in this case I guess the more primitive meaning is "[make something] wet", and the active voice has an extra idiomatic meaning of "to rain".