Though the old Dixie catalog's barrel looks the same, it may not be. The manufacturer, assuming it's the same one, may even have changed their processes between the '50's and '98. It is apparent that Dixie uses multiple suppliers for their cannons, so it's hard to say if the one in question ever came from them at all, though it does appear to be near identical to the picture Zulu found. I think contacting them would be a very good idea.
Also, given the condition of the barrel and the owner's interest in ensuring it's safety, before doing anything permanant, scrape/sand/file off the paint on the muzzle, and if it's lined, you should be able to see the difference between the steel sleeve and the cast iron. Not being an original gun, it won't harm the value to repaint it anyway, so there won't be any harm in checking.