This isn't my area of expertise, so these comments are just from the point of view of someone analysing the evidence.
1. Yes - there does appear to be evidence of the baptism of a Brinsley Barnes, the son of James and Mary Barnes in Ireland. Although as the transcriber states it is very hard to read and this is a transcription of a transcription of the original.
2. Yes the current biographies of Barnes-1138 and Key-172 do state they were married in the American colonies, but both of these are based on Ancestry.com sources and the reliability of such sources is open to question.
3. The current biography for Brinsley Barnes (-1145) is based solely on 1 apparently well-sourced book, and I wonder what it states about his parentage and what sources it quotes (this point didn't seem to be very clear to me at least)
4. Is there any evidence for where the fairly unusual name of Brinsley originates? Barnes-1138 has another wife Mary Sarah Brinsley, which might help explain this, but I don't think there were any sources attached to her at all. Could the son of James and the son of William be related?
5. Don't take this personally, because it is in common usage, but I often distrust comments that start "It is widely accepted ..." - to me that is genealogy speak for 'we think it's true but we don't have any proof' which may or may not be the case for this profile.
If this was a person I was researching (and I'm not offering) I would start by trying to find as much as I could about all the other people involved, William Barnes, Elizabeth Key, Mary Sarah Brinsley etc. Who were they, where did they come from, if they were in the colonies, when did they arrive? Barnes-1138 in particular looks like he might be an amalgamation of several profiles with the name William Barnes.
As I said I'm just evaluating the evidence, and I think currently there is evidence that Brinsley may be the son of James and Mary, but as yet not enough evidence to definitely change the parents. Further research might discover more and make the decision easier.