DI doesn't spit fouling on the BCG any more than short stroke. In point of fact the HK91 fouls the bolt just as badly - it has NO gas action at all. Why? Because of timing - when the bolt unlocks on any self loading action the cartridge is freed up to move to the rear, creating a much larger opening for gas to escape. The brass gets dirty on all self loading actions, which is the proof. Gas escaping past the brass is what dirties the bolt, not a gas tube located above it, partially shrouded by the key in the early portions, and fed by a small .061 port in the barrel. The chamber is huge in comparison and dumps the residue into the action - not the gas tube.
Extraction timing, which determines the amount of blow-by as a case extracts, has nothing to do with gas system type. That's secondary follow-on aspect of the overall dynamics of the gun (as is return spring strength, carrier travel distance, and overall BCG mass). You can have long-stroke systems that have a long enough dwell time, and you'll get no blow by; the earlier designs last century worked this way as a protection measure against case & overpressure failures. Blowback designs, like the filthy 10-22, are especially prone to fouling from blow by, since they extract much earlier than locking breeches.
Pics posted of AK's online show them getting crusty and fouled after a few hundred rounds, too. The myth of DI being a dirty action by it's direction of gas is a 1960's myth perpetuated by those who didn't understand firearms design.
That's because the AK system vents piston gas directly into --wait for it-- the area above the bolt carrier. The piston travels ~1/2", the gas chamber the uncorks and excess gas volume (which is a lot in an AK) flows around the piston inside the gas tube area and into the area beneath the dust cover. That's why excessive backpressure from cans or rechambering jobs in an AK can cause the dust cover to blow off. This is usually, but not universally, an issue with long-stroke systems, since the piston is generally housed in a continuous conduit to fully shroud it (and the piston is continuous with the carrier). Other designs, the RPD comes first to mind, have either a gap between the tight-fitting gas chamber/gas cup and the entrance to the bolt carrier channel portion of the receiver, or very generous venting to the sides or front and below the bolt/chamber area (the BREN was kind of like this)
The Stoner design also has a gas cylinder inside the BCG sealed with piston rings on the bolt. In one respect it's short action - the gas pressure builds forcing the bolt against the breech while simultaneously moving the bolt carrier to the rear. Once the bolt lugs are unlocked further gas pressure of the cartridge against the bolt face adds to the rearward momentum of the BCG. The M16 can extract without the extractor - when timed properly. Gas pressure in the barrel blows the cartridge case out.
I'm not sure why, but there's this whole myth out there about the AR gas system, where pressure at the end of the gas system can be higher than at the gas port. The only way the bolt is getting driven against the breech is if the force behind it is greater than the force in front of it. That means that gas pressure inside the bolt must be higher than in the chamber, but there's the little problem of the gas tube connecting the two. The gas port & tube act as an orifice, dropping pressure as gas flows through them, which further ensures that chamber pressure will always be higher. While the flow can momentarily reverse as the bullet exits the muzzle and the chamber pressure quickly drops, this is both very late in the unlocking cycle and incredibly brief (far faster than the inertia of metallic parts can react). The potential forces involved are also tiny since the chamber/carrier both lose pressure simultaneously after the bullet leaves, reducing the differential between the two that could potentially push the bolt forward. If there were a check valve in the gas key that prevented backflow into the bore, then this 'after pressure' effect against the bolt tail all throughout the unlocking cycle would be believable. However, it would make the 'self extracting' myth alleged of the DI system impossible; the bore pressure must drop faster (almost instantly, which it does) than the bolt carrier after fully unlocking (at which point it is vented at the gas key and internally IIRC) even though its pressure and gas volume are much smaller. Not happening.
The mundane reality of the system is; gas knocks the carrier rearward right as the bullet passes the gas port, the carrier begins rotating the bolt just before or after the bullet leaves the barrel (depending on timing), and if timed toward the early side (roughest on the bolt lugs and extractor) a small puff of gas escapes around the case. No different than any other system as far as those primary/secondary extraction dynamics. I would agree that the AR DI system more closely approximates short stroke operation, because it 1) delivers a brief strong impulse to the carrier early in the cycle, with a mechanical dwell before unlocking the bolt after the driving force is gone, and 2) does not add mass to the BCG assembly as part of delivering this impulse. In a way, it's shorter than short stroke, because no additional mass is added during the driving phase when a short stroke piston is active, meaning a given force will accelerate the BCG faster than if there was a piston/tappet (so you could get away with a smaller gas pressure contribution than with a short or especially long stroke system)
Timing is more important than anything in a self loading action and because it's dynamic it's hard to see and measure. It's much like choosing a camshaft for an engine and I deal daily with self professed experts who can't begin to explain how it's measured or what changes will do to valve timing and the results. It's much the same with velocity from short barreled AR's, some keep repeating that there is huge velocity loss when a barrel is cut down to 10". The loss is a lot less than it seems and why the military still uses the CAR-15 after 45 years. They just call it something else now.
You're right, it is exactly like an engine's timing. But engines aren't timed based on gas dynamics between two connected volumes of gas at different pressures, but by solid mechanical interference of cams and lifters. The closest analog in automotive to what is being claimed in the AR gas system is intake/exhaust back pressure due to acoustic effects in the tubes --and those effects are nowhere near significant enough to impact engine timing (as opposed to pure optimization, which they obviously are). That, or designing an engine to depend on a degree of valve float to time properly.
Some will differ but DI is short piston, and all self loaders spit residue on the bolt. Those of us who own(ed) HK 91's know that and don't repeat fake news.
Oddly, my FNAR cases come out clean, and after 1000 rounds, only the tappet piston area has powder fouling. The oil cleaned at the breech area is tinted grey, vs. black like near the piston area. Fired rounds smoke for several seconds after ejection so some soot escapes during extraction, but it has nothing to do with a higher internal pressure. I'm not sure what an HK roller gun has to do with gas operated locking systems, but I do know a fellow who goes by Holescreek who made a short stroke piston-operated CETME on modified roller-delay parts so he didn't have to make a fluted 243 chamber, and IIRC his brass came out clean, too.
TCB