It gets even tougher if the wrestler has a felony conviction, even if all required paperwork has been properly completed in advance of the trip.
Ron Killing spent a little over a year in jail when he was 19 or so. Likely it was this conviction and record that flagged him at customs in Canada.
Regardless, delays and issues are common at Canadian Customs as you can be denied entry for numerous reasons, many minor and arbitrary. I’ve been held up getting into Winn*peg, Abyss was denied entry once there for no good reason, Kevin Nash was recently delayed 2 hours before being granted entry into Vancouver (several weeks earlier he had no trouble getting through), AJ Styles was delayed once for several hours before being granted entry, and there are numerous other examples.
Many wrestlers are getting to where they hate Canada bookings because of the hassle at customs.