Hi Carol, thanks for that!
We often see this scenario in PGM - we find a baptismal record for a person whose name is the same as the New England immigrant. What we then have to establish is, how do we know for sure that this actually is the New England immigrant, vs. another person with the same name?
I don't think the evidence on his profile is sufficient to settle that question yet (according to the standards RC Anderson and PGM typically use).
The most common type of evidence I've seen in this scenario would be a will, probate, or other deed for Richard, Phillippa, or any other immediate family (siblings, grandparents, uncles) that specifies "Henry, son of Richard, now living in New England" — jackpot, if we can find one of those!
Another thing that's commonly done is to check very thoroughly in Aston Clinton and surrounding areas to see whether Richard's son Henry is recorded as being still in England after our Henry arrived in Woburn. We'll either prove that Richard's son didn't go to Woburn, or we'll show that we've done our due diligence.
If we can't find evidence for Henry directly, we could still strengthen the case with any evidence we might find for John or Richard or any of Richard's other known children. That's what CC Baldwin was doing (in the article you cited) when he speculated that this Richard might have been the Richard named in a court record in Braintree in 1637 (the same man listed in Great Migration Directory, origin unknown). If we could examine that court record and link any of its circumstances back to Richard of Aston Clinton, I'd say knowing this Richard came to New England would be decent circumstantial evidence that his son(s) may have, too.
Bobbie asked a question above that I wasn't sure the answer to — do we know Henry of Woburn's age from any Woburn records? If we're saying he matches a 1623 English baptism then it would help to know that the age of the Woburn man supports a birth around that time (it's safe to assume that English families at that time were baptizing infants, not older children or adults). Do we have Henry's age at death or from any depositions?
I admit I don't know anywhere near enough about DNA to use it as evidence. It sounds like the Y-DNA/FTDNA analysis done so far is sufficient to suggest a connection to a common ancestor of the Baldwins around Aston Clinton, generally, but I'm not seeing anything specific enough in the DNA to link Henry of Woburn directly to Richard (vs., say, a different branch of that family). We still need the other records to flesh out the details of how he's connected to those ancestors. (Any DNA pros want to weigh in?)
To be clear, I think it's fine if Henry of Woburn's parentage is possible or plausible but not proven, and I don't think it's your or my personal responsibility to find the proof. :) I just wanted to check what we know and don't know right now, so we can be as clear as possible on their profiles — and give future researchers an opportunity to improve what we know!