Basically, if they ask, we give it to them. The disclaimer is on the link to the Shed, so they are agreeing that they know they're getting into something different than just a regular area of the board by requesting the password.
We don't verify age or anything - they're telling us they are "of legal age to view potentially vulgar content" by requesting the password.
But the reality is, the Shed is pretty tame. Just a place to vent.
In my time as a Mod I've only not given the password to one person - that was someone who had just joined that day and had no posts. I told them the Woodshed was for members and encouraged them to post some for a while and request it again. I think I gave him the password a week later.