Being intrigued by this, I decided to look into it, and may have come up with a very probable answer for you!
Given that 'Daniel Devonshire' is a fairly distinctive name, I assumed Elizabeth Wilson would've named her child after his father, a common practice with illegitimacy. Seeing as John Devonshire & Mary Harrabin baptised a child, Daniel, in Sheringham I decided to look into their family - assuming a familial connection.
If you had any doubt, the Daniel Devonshire born in Sheringham in 1788 is not your Daniel Devonshire Wilson, as he died an infant in Sheringham in 1788. John & Mary had four children in Sheringham: Elizabeth (1780-1781), Martha (1785-?), Elizabeth (1786-1796), and Daniel (1788-1788). This Devonshire family moved to King's Lynn in the mid-1790s, as this is where Elizabeth is buried. John and Mary were buried in St. Nicholas', Lynn in 1803 and 1808 respectively. John's age was given as 53, giving him a birth year of c.1750. A marriage for John Devonshire and Mary Harrabin is recorded on the IGI as occurring 28 Aug 1775 in Wisbech, Cambridgeshire. John is noted as being 'of Northamptonshire'.
Another marriage in Wisbech caught my attention, that of Daniel Devonshire (of Peterborough, Northamptonshire) to Sarah Walter on 8 Sep 1785. The name Daniel and the fact that both of them came from Northamptonshire led me to think they were brothers. Checking the entries on FreeREG I found that John Devonshire was of Oundle, Northants. when he married Mary.
Northamptonshire appears to be sparsely represented on the IGI, but FreeREG has a much better coverage. There I found John Devonshire, baptised 3 Nov 1747, and Daniel Devonshire, baptised 2 Sep 1753, in Oundle with parents Daniel and Martha. This clinched it!
John and Daniel were brothers, and, given that John moved to the north of Norfolk, it is probable that Daniel at least came to visit him, and maybe wooed a local girl, Miss Wilson...
Daniel did not stick around Norfolk or Cambridge, but went back home to Oundle, where he was buried on 21 Oct 1789, age 36. I do not know what happened to Sarah Walter or whether they had any children together (if they have a surviving direct male line, DNA testing would prove whether Daniel Devonshire was the father of Daniel Wilson).
Hopefully this all makes logical sense. I think it's quite reasonable to assume that Daniel Devonshire was the father of Daniel Wilson, and therefore responsible for all the Devonshire/Wilson confusion in later generations. All the information above can be checked at FreeREG.
Cheers!
P.S. I also came across the will of William Goodwin of Hevingham, who names his son William and son-in-law Daniel Wilson as executors. It's available at
http://www.norfolksources.norfolk.gov.uk/DserveNS/ - just click the probate button and search. (I searched for Daniel Wilson, which brings up fewer results than searching for William Goodwin, and it was the 10th entry, from 1834).