I doubt they get them early from the mint, in fact how could they get them early and have them be first day of issue? The gift shop at the mint is probably able to get the sets on the first day and these HSN people sit there till they come in and then ship them out to ANACS postmarked that first day. They DON'T have them yet. Note in their advertisement that they are on "extended delivery" and won't ship until the end of the month. They may have gotten a couple of sets in from ANACS overnight delivery but my bet is that most of the bulk submission is still at ANACS being graded. That's why they can't ship immediately. They don't have them.
I checked the video, he says they were released 8 hrs ago, not that they received them 8 hrs ago, and that their coins are on their way to the graders, and that what he has on display is a mock-up. THEY DON'T HAVE THEM YET.