If memory serves, the vaccine was based on too much preexisting work to be deemed patentable, yet this unearned attribution to his selflessness as the reason it was not patented is trotted out almost as often as "Qu'ils mangent de la brioche"
Murrow: Who owns the patent on the vaccine?
Salk: Well, the people, I would say. There is no patent. Could you patent the sun?
First off, the patent wouldn’t go to Salk, but the National Foundation for Infantile Paralysis and the University of Pittsburgh. They did in fact get patent lawyers to investigate patenting the vaccine.
Still, I don’t think this makes the Salk quote disingenuous. Salk first refused to even meet the patent lawyers, and when he finally did meet them, he claimed no novelty, and that he used formalin in a long-standing technique so anything new was narrowly oriented to polio and not substantive enough to patent. So it was Salk himself who convinced the lawyers that the vaccine was unpatentable.
Here’s the thing— I don’t think this is quite correct. Certainly in modern medical practice very slight changes are sufficient to have a patent be renewed (this is a genuine problem in the medical industry). While it is unknown if a patent would have held up to prior art scrutiny, it would not have been absurd to try.
Given Salk’s reluctance, It is likely the quote represents his actual feelings on the matter, and he brushed the lawyers off at least partially for moral reasons.
See: Polio: an American story. David M Oshinsky. Oxford University Press, 2005.