My argument was, just because US continuity is an internal mess doesn't mean it can't stand on its own, separate from the JP continuity.
But if that can stand on its own, the combined mess of what the Japanese, Americans, Germans and who else wrote, can also stand together as a single continuity with many inconsistencies. Either way, you're noting inconsistencies, favoring one interpretation, and moving on.
A few, maybe it could be left alone. A lot, like the case is with Classic MM, and trying to say that both regional versions are wholly the same doesn't really work.
Thing is, what exactly is this US continuity? From the top of my head, the first biggest addition/change is the story in the MegaMan manual; the story of assistant Dr. Wily. This story is further recited and added upon in other sources such as Nintendo Power. Kobun20's Reploid Research Lavatory nicely details how this story evolved over time. It's an interesting read, especially if you really value the story as it was originally told in the US.
However, there are also sources in the US continuity that tell of the story as it is told in Japan; MegaMan8 and MegaMan and Bass come to mind. So, either one acknowledges a conflict between those two stories, or one considers them as adding to each other to paint a complete picture.
In the above example, there is no conflict between US and Japan continuity that does not exist within the US continuity itself. As such, there's no need to consider them as separate entities; the US continuity would be the same as the Japan continuity with some added stuff.
Many other things in the US continuity are solely additive; the name of the time institute, the name of the time machine, the time Wily traveled to the future. This is in no way contradictory with what the Japanese text says, and thus can help shape the overall mythology of the series, even if it is not mentioned in Japan. Something similar has happened in X1, when the Japanese took the US-written MMX1 manual and made it their own with only a few alterations.
What else is there? Some of the boxes mentions the characters as cyborgs, but that is also inconsistent with the US continuity itself; as an inconsistency, we do not consider it valid, and it makes no difference in the question of "one continuity versus two".
The only thing that remotely could warrant the existence of a second continuity is the rewrite of the actual game script instead of translating as should be. See: MM7, MMX2, MMX5. However, the same was done in such classic titles as "A Link to the Past" and "Chrono Trigger". Both games have seen a ported rerelease in recent years, with a completely retranslated script, that rectified many of the inconsistencies and yes, "mistranslations", that existed within the originals.
So, what do we do with this? It's easiest to see it all as a huge mistranslation and only the Japanese as bonafide fact. But, for all I care, the altered US script is some strange timeline split akin to IHX's two X playthroughs where everybody for some strange player input reason happens to say different thing, that are still somehow valid. You know, how bosses will say different things to X because you selected a different difficulty?
Like I said before; game stories are entirely linked to player input. What the player does can change the way the plot moves, and it is always unclear what the sequel actually goes by. As already evidenced by such titles as RockmanEXE: this player input of buying a specific version does not make a new canon or continuity. So if you really wish to include information as factual; just consider it the epitome of player input to buy the American version over the Japanese version, and consider both as valid. Just like one shouldn't really care which X playthrough of IHX actually happened, or which EXE game you actually bought.