Why you you say dubious history ?
No disrespect to car or owner, or even OP, but what would you call a car that has no paperwork and no proof of history with a wild claim (true or not)? Not disputing the claim. Over and over, as you well know, guys on this site and Yenko say a car needs docs. If the owner’s assertions are all that back up this car’s history, and long time ownership can lend credence, then, while sad, there will always be a footnote of alleged which is why it fits my understanding of the word.
From Webster’s-Dubious:
1. doubtful, “uncertain, unsure,” in doubt, hesitant; More
2.
“not to be relied upon”; suspect.
"extremely dubious assumptions"
synonyms: suspicious, suspect, under suspicion, untrustworthy, unreliable, undependable, questionable;