My 700x23 Schwalbe One V-Guards arrived folded like the second video demonstrates. The tires were from 2014-'15 and had probably been stored that way for years. There were minor crimps but they fluffed out when inflated. No problems in about 1,500 miles of riding this summer and autumn.

I may put those tires away until next spring so I'll fold 'em back the same way.

I've received wire bead tires packed exactly as shown in the first video. Again, no problems. On long rides on bad roads I've taken a spare wire bead tire folded that way too. Any minor crimps and fold marks fluff out when inflated.

Or just hook 'em across a hanger and hang 'em in a closet, the garage, wherever you have room. I've done that as well, no problems.