Protecting yourself with a purchase
Was the inspector someone who knows Airstreams, restored an Airstream, and/or knows all the pitfalls? If not, then the inspection you receive may be just a surface look. Do you know all the pitfalls of buying a vintage trailer - hidden floor rot, frame rust that needs to be repaired, axles, tires, appliances, general leaks, etc. Do you have close up pictures, video, etc. I would never buy a trailer with plans to use it as is without inspecting it myself.
As a buyer and a seller of vintage trailers and Airstreams (bought and sold four, and have kept the fifth for now. ), it's been a deposit and then finally payment (sometimes just a check, cash, Ebay, or wire transfer). The buyer is given a bill of sale or I ask for one, then title if available signed over or mailed. It depends on what the seller is willing to do in terms of cash and paper work, in my mind. If you are not happy with the terms, don't buy the trailer. There are plenty out there and possibly near by.
Posting on one of the Facebook forums, Airstream restoration sites, with good pictures, can provide you with possible issues.