I may have watched the same video. I actually watched several of them. I watch one about 1/3 of the way through before determining the guy had never done it before himself in that it took the 1/3 of the time trying to get the back cover off after all of the screws were removed.
Anyhow, one of the ones I watched, the guy suggests the use of a hair drier or "Heat Gun" if you have one. This will loosen the adhesive. He does make a point to warn you not to mess up the flex ribbon that operates the "Settings, Home, Back, & Search" soft-touch keys at the bottom of the phone. He states that if the screen is broken, you really don't need to worry about taking it off in one piece anyway. Just make sure you don't mess up the flex at the bottom unless you plan to replace that as well.