No, Faramir's resistance to the Ring had nothing to do with his heritage. It was a result of his personality: he was humble and modest, where his brother Boromir was vainglorious and proud. His ability to reject the Ring may also have been related to the fact that Tolkien identified with Faramir more than any other character.
Frodo saw it:
Yet [Frodo] felt in his heart that Faramir, though he was much like his brother [Boromir] in looks, was a man less self-regarding, both sterner and wiser.
- The Two Towers; Book IV; Chapter 5: The Window on the West
Beregond saw it:
"[Faramir] is bold, more bold than many deem; for in these days men are slow to believe that a captain can be wise and learned in the scrolls of lore and song, as he is, and yet a man of hardihood and swift judgement in the field. But such is Faramir. Less reckless and eager than Boromir, but not less resolute."
― Beregond, The Return of the King, Minas Tirith
Tolkien saw it:
I think you misunderstand Faramir. He was daunted by his father: not only in the ordinary way of a family with a stern proud father of great force of character, but as a Númenórean before the chief of the one surviving Númenórean state. He was motherless and sisterless (Eowyn was also motherless), and had a 'bossy' brother. He had been accustomed to giving way and not giving his own opinions air, while retaining a power of command among men, such as a man may obtain who is evidently personally courageous and decisive, but also modest, fair-minded and scrupulously just, and very merciful. I think he understood Eowyn very well. Also to be Prince of Ithilien, the greatest noble after Dol Amroth in the revived Númenórean state of Gondor, soon to be of imperial power and prestige, was not a 'market-garden job' as you term it.
- The Letters of J.R.R. Tolkien, #244
From the article on Faramir on Tolkien Gateway:
Faramir was, in the words of Tolkien, "modest, fair-minded and scrupulously just, and very merciful" [Letter 244]. His appearance toward the end of The Two Towers apparently was as much of a surprise to Tolkien as it is to his readers. "I am sure I did not invent him," he wrote. "I did not even want him, though I like him".
Faramir in many ways speaks for Tolkien, who was a soldier in World War I, when he says, for example, "I do not love the bright sword for its sharpness... I love only that which they defend" [The Two Towers, Window on the West]. Much later, Tolkien would write, "As far as any character is 'like me', it is Faramir".[Letter 180]
Faramir himself actually explains why he doesn't want the Ring (in fact, he orders Frodo to not even show him the Ring):
"I would not take this thing, if it lay by the highway. Not were Minas Tirith falling in ruin and I alone could save her, so, using the weapon of the Dark Lord for her good and my glory. No, I do not wish for such triumphs".
- Faramir, The Two Towers, Window on the West
This echoes Tolkien's disgust, late in WWII, at what he described as the allies' attempt to "conquer Sauron with the Ring":
An ultimately evil job. For we are attempting to conquer Sauron with the Ring. And we shall (it seems) succeed. But the penalty is, as you will know, to breed new Saurons, and slowly turn Men and Elves into Orcs. Not that in real life things are as clear cut as in a story, and we started out with a great many Orcs on our side.
- The Letters of J.R.R. Tolkien, #66.
For more information about why the Ring corrupts some people but not others, see this answer.