Tinning is also a term for applying a very thin coat of soft solder. Usually to both parts before clamping together and then heating & joining.
Any Parkers I've ever had apart were only 'tinned' in the area of the contact between the ribs and the barrel surfaces, not the entire surface inbetween the ribs. Can't think of any make of bbl sets that looked covered entirely on purpose inside there.
Wouldn't be a bad idea to avoid rust though.