Following your argument they would be allowed to take all your stuff and sell it on ebay because you didn't sign anything. What applies is their standard rules

Following your argument they would be allowed to take all your stuff and sell it on ebay because you didn't sign anything. What applies is their standard rules, whether you signed them or not. In fact, because you didn't return the signed document clearly shows carelessness or malice on your side and will play against you.