Some years ago when I was searching for a caravan I had similar problems in that everyone said their caravans were damp free, or at least when asked would make some non-committal reply like, 'Not the last time I looked' or 'Not as far as I know'. One person replied by saying they put their bedding in the lockers under the front seats and it was never damp 
I didn't have the benefit of a damp meter but it took literally months to find a dry van and even then I discovered after buying it an area that had been damp at some time. Fortunately I found some paperwork among all the paperwork I was given to show it had been traced and repaired a couple of years previously.
One thing that would trouble me with damp meters at this time of year...is it possible that they could pick up condensation on the inner walls rather than damp within the walls?
I had similar problems a little while ago when I was looking to buy a motorhome...not so much damp but every single one I looked at had oil dripping off the bottom of the sump. I never did find one that didn't have some potentially expensive problem and eventually gave up and bought a new car and a tent 
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