The "accepted wisdom" I'm referring to has been around as long as semi automatics, and it is that, by the very nature of their mechanisms they are more ammunition sensitive than a manually operated action.
Quite literally the manually operated action will cycle the same (because the shooter cycles it) whether the ammo is full power or just barely enough to have the bullet clear the barrel.
While there are limits, the manually operated arm also can be "force fed" better than most semis.
I was amused by the video describing the recoil of an 8lb+ 5.56mm as "vicious".
Lots of running around rapid firing at pistol ranges, which showed that, for that it seems like a good tool. Didn't see anything relating to actual riflery or reliability other than other than discussion about piston vs direct impingement gas systems, which was nothing new to me.
The HK 416 seems to be a good improvement over the original AR system, but I found nothing in the video or the articles you linked comparing it to anything other than the M16 system for reliability.
Show me where the HK jams less than a Mauser 98 (without operator error) and I'll consider it.
I've got extensive experience with the M14/M1A, M16A1, FAL, HK 91 AK 47 SKS, SVT 40, M1 Garand and others, numerous smgs and semi auto versions, every small arm in standard US Army use in the mid 70s, I was a Small Arms repairman (meaning I worked on everything from the 4.2in mortar on down) for Uncle Sam, and I've studied machine gun design as a hobby for almost half a century.
Every one of them has the same unavoidable Achilles heel, they won't run on ammo outside of their design parameters, while a manually operated firearm, has a wider range of tolerance.
When I think of reliability, I think of military bolt actions, Mausers and such with their massive claw extractor and SMLE's with their "generous" chambers that ensured that a round with what ever crud it carried went in, fired and came out.
I think of Double rifles, where the entire second gun was built in to ensure one of them worked, no matter what.
The HK 416 might well be the most reliable semi auto but an 8lb 11in barrel .223 with a $3,200+ price tag PLUS needing the Federal license for an SBR just isn't for me, no matter how reliable it is.