Are the 500 and 870 barrels capable of fitting either shotgun? Owned a Mossberg 500 for years. Can someone settle this urban legend?

nope, not a direct replacement.
if you have a fully tooled machine shop thats a different matter.
if you have a fully tooled machine shop ... you may make a barrel for either

Mossberg made some aftermarket replacement barrels for the 870. These do not fit mossberg guns, though.

What both the gentlemen above said. Urban legend. One company used the other company at some point, as a trustworthy sub-contractor.