I didn't comment last summer when this topic was posted, largely because I know nothing of the Perrot/Perrott surname or any of the Tudors. But since it's re-energized itself the past several hours... What I can offer an opinion about is the aspect of DNA. And there's something about yDNA that I think might be helpful to clear up.
"I have seen their DNA and they match my own about 23/25 first markers then depart to a cousin line status sharing only 55 of 69 markers on Y chromosome. This difference is due to my line having a Sutton Dudley heritage as in Sir Robert Dudley."
If I read this correctly, a supposition is being made that yDNA can show a degree of STR commonality and then diverge significantly along descent of a family tree. It cannot. The Y-chromosome escapes crossover during meiosis and remains haploidy at zygosis; a new diploid genome is formed that includes every nuclear chromosome but the Y. The Y-chromosome is solely from patrilineal inheritance and the only way it changes is via mutation, not recombination or DNA sharing.
It is possible for men to look like matches at a low testing resolution, for example 12 or 25 markers, but not share an ancestor in the genealogical timeframe. We most often encounter this in males who have a common set of STR repeats, like the Western Atlantic Modal Haplotype. Unlike autosomal DNA, though, correlation on the Y is not affected by percentage of DNA shared. STR matching is not additive, it's cumulative...and it's about estimated genetic distance: an STR marker isn't either a match or not a match; the number of repeat differences has to be evaluated, as well as whether or not the markers differing are multi-copy, palindromic markers where the infinite allele model would come into play.
Without knowing what actual STR values are involved, no one can make an assumption about matching only from the fact that 23 of 25 markers were the same. At 25 markers, a genetic distance, or GD, of three already moves the match out of likelihood in the genealogical timeframe.
But each panel of tests continue to refine the possibility of a relevant shared ancestor. At 37 markers, FTDNA will describe a GD of 5 as "possibly related," and a GD of 6 as "not related." At 67 markers, a GD of 8 or 9 is "only possibly related," and 10 is "not related." If carried out to further resolution with a greater number of markers tested, it doesn't matter whether or not two men were considered a possible match at 25 markers: if the evaluated genetic distance at 67 markers shows that they are not related in the genealogical timeframe, they aren't.
In my own case, we have a total of 31 matching men in our yDNA project (a subproject of the extremely large Williams DNA Project), 16 of whom have taken the Big Y full-sequencing test and a 17th whose full-sequence results are pending. Among us are 20 with the surname Williams and 11 with four different surnames. The full-sequence tests have allowed us to understand roughly what this ancestral tree looks like. The earliest in-common SNP is R-BY22194, and we believe the split into all five surname lines occurred sometime after 800 AD but before 1100 AD. This is outside the genealogical timeframe and occurred in the British Isles before surname adoption.
The point here being that, by way of example only, for STR matching at 67 markers I have these identified, other-surnamed men: two at a GD of 4; one at GD 5; two at GD 6; and three at GD 7. And we know the most recent time we would have shared a patrilineal ancestor is circa 1000 AD, more likely 900 AD. Nothing is impossible, but it is highly, highly improbable that two men who share a common ancestor born circa 1565 would not be within genetic distance for a Y-STR match at 67 or 111 markers.
I did look at the Parrott/Perrott yDNA project at FTDNA. There is one kit there with the surname Rice in the Ungrouped area. I don't know if this kit is pertinent to the discussion here, but looking at the first 25 STRs the only Group shown to which this Rice kit might possibly be associated is Group "I1a, Francis Parrott of Chowan Precinct, North Carolina," and even then the Rice kit is GD 3 from that Group's modal. From those data--at least what is publicly displayed--I can't see any evidence of a definitive connection between the Perrotts described here.
What looking at the FTDNA project did lead me to is a Guild-registered One-Name Study that has been underway for at least 12 years, http://www.p-rr-tt.org.uk/, referring to itself as "The P*rr*tt Society." Clever use of wildcards. They even produce a quarterly magazine for members.
The Society has a page where the history and lineage of the lines are discussed: http://freepages.rootsweb.com/~parrott/genealogy/pembrokeshire.shtml. I can't comment because, again, I know nothing about these families. This shows Sir John Perrot (1527-1592) married twice, and had "a number of illegitimate children" including, with Sybil Jones (ferch Rhys): "John, b ~1565. In the Inner Temple Register, there is an entry, dated 5 June 1583--'John Perot, of Haryve, Co. Pembroke, 3rd son of John Perot, Knight'. Possibly also the son of Sybil Jones. He died without issue." The Wikipedia page for Sir John Perrot provides some information about how the rumor began that John was a bastard son of Henry VIII; one reference used there is a 2010 publication by The P*rr*tt Society.
I chimed in only about the yDNA matter, and I can find no DNA evidence presented here on WikiTree, on Geni (the profile there shows this John Perrott dying at about age 18 or 19 without issue), or at The P*rr*tt Society that seems germane to John Perrott (~1565-1665, Perrott-112) or his father Sir John Perrot (1527-1592 Perrot-4). In a quick Google search, I could turn up nothing that seemed reputable regarding a yDNA study that included Henry VIII.