I have heard about pushing and pulling keys to feel for softness and play as being a test for poor materials.
A person might bring a tech or sax expert along to the play test.
You could check photos of the prospective purchase against saxpics
http://www.saxpics.com/?v=gal&a=3060
which is, I think the most modern of the baritones King made.
There is also Keilwerth New Kings and some other brands used the word King (royalty being a selling point (?)).
You can hunt these up in saxpics, also.
Personally, the story, price and photo combo would make me plenty nervous about throwing money away ...
[too good to be true story from me: Pristine old Bb bari for only a few hundred dollars from newspaper listing, wonderful horn. Turned out to be HIGH PITCH! Whoops.]