Honestly, I think I do understand the point you were making, but I think it gives completely wrong advice about sourcing, and I don't think you are understanding my explanation about why.
The question is whether the sourcing is good enough to justify the new information added to the American profile. That new information connects the American to an English event. And the answer is no, that sourcing is not good enough for that new information inserted into Wikitree.
There is no appropriate source that has been given, and probably there is none, for the information that has been put into Wikitree now. That is surely the key point here?
The way I read it, you are in a circle of repeating that this would be a different subject, but I think you are wrong about that, and you should reconsider. It is not just a question of the fact that no parish register has been properly cited, but also that no parish register can tell you someone migrated. There is no other subject raised by the original post as far as I can see.
Whenever we ask whether a source is good enough, we always have to look at what it is being used for in Wikitree, which is a migration claim. No source in the world is good for every possible purpose. So I am concerned you are ignoring the purpose of this proposed sourcing, which is to equate specific people in America and England. You shouldn't ignore that.
There are indeed some sources on Family Search which are good for certain uses, but this is not a useful or appropriate point to be making in my opinion. Sources should be judged according to the intended purpose.
We have to look at whether a specific source is being used here in a way which justifies a specific edit. The answer is no as far as I can see.
Various theories about John Gowan Lancaster were discussed a lot some years back by Nancy Matthews and others but many of the old forums (mainly genforum?) where she posted are now gone because of the changes in the various companies and websites.
In the Lancaster DNA project we worked with Nancy quite a lot on some of these questions. As far as I recall this was all still speculative? In any case, before adding a major claim, we need to have all the evidence and explanations prepared. This is a major claim.
Unfortunately however this is one of those families where there is a lot of internet copy-paste style work which creates a constant confusion because the original notes and reasoning are rarely kept or understood. We all know many profiles with such problems tend to be profiles which are claimed to be immigrants to America, exactly like this case.
This way of working which connects up people from totally different places, without checking whether there was good evidence or not, is a long-run problem in all internet genealogy, which we are all now trying to clean up and be more careful about.
I am obviously not against explaining what the leading speculations are, but that is not being done here. To break the circles on some of these speculative migration claims we need to lay out the reasoning for any speculation which we want to insert into Wikitree.
We should also be looking to see if the English Lancaster which we are now merging into the American one perhaps has a profile already.
Equating two people from different continents is not something we should not do lightly. But that is what has been inserted into this article.