But this/that is not to say is the collocation. In your version, the expression lacks a subject. " In this case you have a compound predicate.
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meantolearn"His position is to recommend the treatment for old folks, but (his position is) not to say that young folks couldn't benefit from it."
Is this what you suggested, the same subject? Yes - just an optional solution to show that it's not absolutely necessary to add "that is."