The book 'Pucketts and Their Kin' is on Internet Archives here: https://archive.org/details/somepuckettsthei00garr.
This book was privately compiled and published by Hester Elizabeth Garrett in 1960. It certainly has some great research, but in double-checking the records cited, there are some serious mistakes which have thrown off Puckett researchers for decades.
I will eventually try to make a full list of the mistakes, but a few in particular are the most egregious.
Page 2 - Marriage of James Westbrook and Elizabeth Westbrook did NOT happen ca 1678-9. Garret cites the wrong record book, but correct page number. The record is in record book Henrico Co, VA Wills, Deeds, etc. (which I abbreviate WD) 1697-1704, page 96. My full abbreviation is Henrico Co, VA WD 1697-1704:96. This book is sometimes erroneously called WD 1697-1699, but that is just the 1892 copy, which only copied records before 1700 (In the late 1800s, genealogy was becoming popular, and the old record books were falling apart from being handled so much, so Virginia had many of the pre-1700 records hand-copied. The copies of Henrico records were made in 1892.)
The marriage record of James Westbrook and Elizabeth Westbrook is in Henrico Co, VA WD 1697-1704:96. FamilySearch has images of the original (digitized film 007645094:51) and the 1892 copy (007676115:171). The original is too difficult to read, partially due to the original record fading, and partially due to poor microfilm photography. The 1892 copy is legible. There is a list of probates and marriage licenses under the heading 'An Acct of Probat admcon Returned to Mr Sectys office Aprill ye 13th 1698' (An Account of Probate Administration Returned to Mr Secretary's office 13 Apr 1698). One of the lines below that heading is for a marriage license:
Jany 3rd 97 James West Brook with Eliz. Puckett
This license was granted 3 Jan 1798 the way we reckon dates now. See my article on Old Style Dates for why it was written as 3 Jan 1797. James Westbrook and Elizabeth Puckett may have married the same day the license was granted, but likely the wedding was a few days later.
Note that Garret also says the marriage of Thomas Jefferson with Mary Field was in 1678-9 on the same page as the James Westbook & Elizabeth Puckett marriage. However, the marriage license for Thomas Jefferson & Mary Field was granted 20 Nov 1697, which is a well-known fact given these were the grandparents of President Thomas Jefferson. In the 1892 copy, the marriage license is recorded 3 lines above the Westbrook license with date '9br ye 20th 1697'. 9br was an old abbreviation for November.
Page 23 - Reported record for "Tyree Puckett" was actually for Gyll Furkett (Gill Fuquett). Garret cites Henrico Co, VA WD 1672-1692:70, which is a bad citation, because the book is actually WD 1677-1692. Garret must have got her notes confused, because she says the record is something about Tyree Puckett being a neighbor of Abraham Womecke (Womack) and Richard Kennon, dated 9 Mar 1678.
This was actually a list of people accused of various infractions by sheriff Samuel Knibb; these infractions occurred at various times in 1678 and early 1679. Many of the people were accused of public drunkenness, including Abraham Womack. One of the lines in the list says "Aprill ye 21st [1678] Gyll Furkett told me that he was drunke" (007645093:18, 1892 Copy: 007642295:21). I guess Garret misread this as Tyree Puckett.
The pre-1700 records of Henrico Co, VA have mostly been fully indexed. There are a few other references to Gill Fuquett or Gyll Furquett. This appears to be a French name, and there were many French Huguenot refugees in Henrico Co, VA. In old handwriting of the time, F at the beginning of a word was often written as a double-f, so it looks like "ffurkett" which looks kind of similar to Puckett. However, this was not a Puckett reference, and there was no 'Tyree Puckett'.
Page 23 and Page 7 - William Puckett did NOT have a will dated 20 Nov 1682. This stems from a badly abstracted deed record, Chesterfield Co, VA DB 1:534 (008578886:272, note you need to go to the Tools button and adjust the image contrast and brightness to read it). In the deed, Lewis Puckett of Amelia Co, VA sells land to William Walthall on 17 Feb 1753. The deed states “which said tract of 108 acres of land was given to the said Lewis Pucket by the last will and testament of his father William Pucket as more fully appears by one patent bearing date 20 Nov 1682”. This does NOT say that William Puckett's will was dated 20 Nov 1682. It says there was a patent dated 20 Nov 1682, meaning the land in the deed was part of that patent.
This was a reference to VPB (Virginia Patent Book) 7:200 (008570201:205), dated 20 Nov 1682 for 757 acres to William and Thomas Puckett. A close reading shows that 500 acres was from the patent to John Puckett (father of William and Thomas), VPB 5:482 (008570200:780), copy in VPB 5 (Copy):589 (008570199:595); patent in 1665. The other 257 acres was new land.
It was quite common to reaffirm old patents when getting new patents as a way to remind the colonial government that one had legal title to the land. An agreement contract between William Puckett and Thomas Puckett in Henrico Co, VA WD 1688-1697:3, dated 12 Oct 1688, states that Thomas and William inherited the 500 acres by the will of their father, John Puckett. The will itself is lost, but is mentioned in Henrico Co, VA court records.
Anyhow, Lewis Puckett was the son of William Puckett Jr, son of William Puckett who, along with brother Thomas, had the 1682 patent. Lewis Puckett was merely stating that the 108 acres he inherited from his father William Puckett (Jr) was part of the 1682 patent granted to Lewis's grandfather, William Puckett Sr, and great-uncle, Thomas Puckett. William Puckett (Jr) died in Henrico Co, VA in June 1739 (see Chesterfield Co, VA Chancery Case Case 1764-002, William Walthall vs Thomas Pucket). William Puckett (Jr) made a will which is mentioned in a few records, but the record book with the actual will is lost. In any case, his will was not dated in 1682.