Yep I went down that path. Every one I contacted about it said no way, some of them even wanted a copy of my title in order to store even a vehicle there. F that. I possibly could have done it if I'd lied but I wasn't going to risk that.
The reason why they want the title is because if they decide to auction off the contents of your storage unit, because of non-payment, then they need the title in order to sell your bike legally.
Without the title in hand, they are not going to go through the trouble of getting a copy of it, plus, it allows them to tell the potential bidders that your unit contains a vehicle, and it is worth more, since all the auctions are blind until the bidding is finished.
BC.