No they wouldn't because that stuff can be faked quite easily, especially online. Most sites don't allow for giving away/trading/selling accounts because it is difficult for the site to prove beyond a shadow of a doubt what truly happened and it becomes a matter of one person's word against another. DW staff would have to use information that can't be forged to prove ownership, and that's going to be login records and records of information changes on an account.

And if you think it's fucked up that people will do it, sadly it happens a lot. I've seen people get fucked over by friends and family all the time and it's usually because of some petty argument. Most companies don't want to get in the middle of personal disputes, so that's why they take the stance of it's the owner's responsibility. DW's only responsibility as far as security goes is to ensure that information that isn't publicly visible isn't leaked.