Most timesharers who use these multi-state closing companies have no clue as to whether the deed that has been recorded for them is valid to pass title in the state where the timeshare is located (?), so their responses will be just what they see on the surface.
Having been on another side of the situation as an HOA officer as well as having a legal background, however I see things from a different perspective. A number of HOA's in our area became concerned about how the deed chain from these out of state multi-state timeshare closing companies in most cases contained at least one deed that was ineffective to transfer title. That can create headaches for the HOA's down the road. When going through PCC's, these closing companies usually produce two deeds in the chain.
The question I would demand an answer to is the name of the person who will prepare the deed. Once you get that, look them up on the State Bar list of the state where the timeshare is located (?). If the name of the deed preparer is not there, you have a rogue closing company, which in many states is actually violating criminal law in their actions. In that case demand a properly qualified closer. If they balk, complain to eBay AND to the State Bar of the state where the timesshare is located.