After some digging, I found this:
I interpret that text as "the filter has a lower bypass cracking pressure and/or higher bypass flow so when you rev your race engine to the moon, you don't lose oil pressure from overwhelming the media or from the bypass not being able to flow enough."
It seems plausible to me then that the original HAMP claim was "reduces oil pressure loss at higher RPM" and over the years of making it around the internet, the "reduces pressure loss" turned into "raises oil pressure" as if just slapping on a different filter to the same lube pump and engine would magically bump up oil pressure. Which we know logically just cannot happen.
Moreover, the pressure loss improvement is present in a filter that just happens to be smaller. The physically smaller size is not the reason for the claimed pressure enhancement. Indeed, less media area would tend to INCREASE restriction, which is why you are correct to raise your eyebrows at the apparently claim that somehow a filter with less area can raise operating oil pressure. That's not reasonable and your spidey sense is not misleading you.