Nick, I've read your informative posts on this board with interest and appreciation. I find myself astonished (and slightly flattered) that I knew something that you didn't.
I think that the reason what I've said is so with the Hornady checks is as follows. By design, they clamp onto the base of the bullet during the sizing process. To be able to do this, they must flare out a bit on the lip. This gives them a bit of +/-.
Not too awful long ago, I looked at that "system" that a guy down in California sells for making one's own gas checks. I was a little put off that he was not selling them at a set price. At the time, he was selling them on Ebay one at a time, with a high starting price. He was metering them out slowly to keep them scarce. The recommended stock for creating the checks was aluminum beverage cans. For a number of reasons, I decided I didn't want to go that route but I admit that was before a box of checks cost $30. Based on the design of the tool and material used, the aluminum checks wouldn't've been of the clamp-on design such as Hornady. Mind you, a separate tool set was required for each caliber.