The video is utter b0llocks. I've removed & refitted necks many many times and this has never been a problem. Opening up the holes in the body might run the risk of the neck shifting in the pocket - especially on a 70s Fender with an overgenerous pocket.
Just received my order. It appears to have come from Sweden rather than Ohio and there were not charges to pay. The tools look to be top quality and it only took eight days from ordering to delivery.
It's the same workshop with the original workbench where Leo worked when it was the original Fender factory, so a lot of classic Fender design work was originated there too.
It will be interesting to see whether Fender keeps Leo's workspace intact — or if his tools etc went in the skip, and whether they put the fullerton factory up for sale, keep it as a factory, or turn it into as museum or other public venue.