Pro
The Hertfordshire baptisms name and date of birth of January 1749 seem about right given his marriage in September 1770 in Alton. Also the name Jesse is used in this Ayling family of Hampshire over many generations and is a somewhat unique.
Also while David's two sons, James (B. 1774) and George (1782-1831) remain in Alton, James' son, Jesse (1801-1888), is living in Berkhamstead, Hertfordshire in the 1851 census. Jesse's oldest daughter Sarah Jesse Ayling is said to be born there in 1840, so Jesse would have been living in Hertfordshire from at least that time. Jesse marries Jemimma Attfield in Somerset in 1831, so we might assume he had left Alton even before 1831. It could be a simple coincidence that Jesse (1808-1888) chose to move to Hertfordshire. Jesse, his alleged grandfather would probably have been deceased by 1780, but there could have been some kind of familial link maintained to that area, perhaps via the maternal line.
Cons:
Hertfordshire seems to be too far north (over two counties) from Hampshire to be right. It could be that father Jesse of Hertfordshire was born there. There is a John & Elizabeth Ayling in Sandon, Hertforshire having a son Thomas in 1750, and daughters Elizabeth in 1753 and Sarah in 1757. Jesse, father of the David baptized in 1749, could be a brother and from a completely separate Ayling family living there with no obvious links to Hampshire. The "Jesse" name could be just coincidental.
Further support for a separate family line is that there are earlier records of AYLINGs in Hertfordshire:
England & Wales, Christening Index, 1530-1980
Birth, Marriage & Death
Name: Mathew Ayling
Father: Matthew Ayling
Baptism: 24 Aug 1633 - Barley, Hertfordshire, England
Name: Susana Ayling
Gender: Female
Birth Date: 14 Jun 1668
Baptism Date: 5 Jul 1668
Baptism Place: Aldenham,Hertford,England
Father: Rich. Ayling
Mother: Mary
FHL Film Number: 1040851, 1040852
Name: Mary Ayling
Gender: Female
Baptism Date: 1 Dec 1735
Baptism Place: Great Amwell,Hertford,England
Father: John Ayling
Mother: Sarah
FHL Film Number: 991303
A reference in the 1871 census to a Richard Ayling born about 1800 in Cradeley, Hertfordshire.
The above are using the ancestry.com search engines. There are possible variations of "Ayling" mixed in with the above such as Eeyling and Aling.
Perhaps the answer is that David was born in Buriton or Petersfield and his baptism was not recorded.