Remember that time you found out that the Easter Bunny was a fairy tale? That Santa Claus was really just your mom and dad? And that your little brothers and sisters weren't really delivered by a stork? Well, if those truths were difficult for you to swallow then I'm afraid I have one more unpleasant truth that you must face as part of growing up.
This advertisement shows a pronounced crimp on Hornady gas checks. I hate to be the one to tell you, but it's a white lie.
Here's a cross sectioned Hornady 45 check. It's not relevant to our discussion but when I took the picture there was a burr on the bottom of the concave base that makes the base look thicker in the middle than near the edge. The base is actually fairly uniform thickness. Anyway, there's no "crimp" in sight. The sides of the check are more or less uniform thickness.
So why do Hornady checks grip better than your Grandpa's slip-on Lyman checks? Because they're thicker. The thicker check gets "squeezed" more in the sizing die. And that's all there is to it.
Sometimes, Even Hornady or Gator checks are not thick enough to get squeezed in the sizing die. For example, Hornady 45 checks are made for 45 pistol, not 458 rifle, so the OD of the check is only 0.4595" or thereabouts. A 0.460" die will not even touch it. Gator offers a solution with its true 458 check (Gator also makes a 45 check which is similar to the Hornady 45).
Check fit is mostly a matter of convenience at the reloading bench because when you fire the cartridge the check shank obturates. Then the check gets squeezed even tighter as it is engraved by the rifling. Unless you are shooting extra wimpy loads that don't obturate even a little bit, all checks should fit snugly by the time they exit the barrel, even if they were a little loose before firing.