This was predictable error on their part. Everyone could see how limited Jones was--even in their "playoff year", where they went 3-4-1 after the bye. 15 passing TDs, 3200 yards (a good season, for him). They were bereft of talent on Offense. Sticking with Jones could only result in the prolonged death that team is dying.
If the owners of the Giants didn't think Daboll "made" Josh Allen, do they hire him in the first place? They certainly would not have kept Jones unless they believed Daboll could "make" him too.