Daniel Freeman married Mary Ledra 15th December 1720 at Lelant.
All I know about them so far is that they had two children buried at St Ives:-
Martha 1729
Thomas 1730
A quick check of things before I call it quits for the night.
IGI
Elizabeth d/o Daniell & Mary Freeman bp. 26th August 1738 St Ives
It would appear Thomas Basset was about 18 years older than Elizabeth Freeman so we do need to query whether he had been previously married.
It may be more likely that they originated from the Mainland with some of the family later returning there from the Scillies.
AND HERE is another little thing to think about.
I visited the Scillies back in 1994 and stayed with my cousin Gail and her family.
Whilst there I did as much research as I could on the Trewhella family who were, and had been, there.
There was one particular burial I wanted to find - that of a James Trewheela whose Will was written in 1699 as 'of Scilly'.
His Will names brothers and other relatives in Towednack where he bequeaths property to said brothers and other kin.
Unfortunately I could find nothing more about him, or his time (however long) on the Scillies.
I soon found the main reason for this.
To my current knowledge there are
no Parish Registers surviving for the Isles of Scilly prior to 1738. So I would not discount the Scillies as a possibility for your Thomas of c.1720.
If it can be established there were Basset people out there prior to then - I think you have a case for consideration.
Never leave any door unopened.
And a quote from my Cousin Nancy:-
Think of every possibility you can, no matter how outrageous, and then eliminate each possibility (as information provides) until you arrive at the only possible and logical answer.
Once you get to this point, of course, there is still the chance of new information surfacing to prove you wrong but ...
Must discuss this problem some more - but at a later date and time I am thinking.