Disabling the protections can technically be achieved. I say technically because there is not one scenario that Airbus has envisioned that would require the pilots to deliberately go into direct-law.
The imposed limit in the question is something called alpha-protection -- a protection against pulling back too much that the plane stalls. Stalling is bad. The system was receiving the correct information and functioning as designed, so what did Captain Sullenberger mean?
Sullenberger said that these computer-imposed limits also prevented him from achieving the optimum landing flare for the ditching, which would have softened the impact.
This is what Wikipedia says. The reference is a Talks at Google lecture (around the 40-minute mark). What is left out from Wikipedia, which Captain Sullenberger covers in the talk right away -- and is present in the accident report -- is that the issue was not with the protection, but with the innards of the protection that Airbus did not cover in the training material. Below is the relevant section from YouTube's transcript:
I was commanding for more, pulling back full aft on the stick and the flight control computers prevented me from getting more lift therefore we hit harder than we would have (...) It turns out there's a little-known software feature known only then to a few Airbus software engineers, and to no pilots to no airlines that was the case. It's called a phugoid mode. And it was not the way we were trained the airplane should work, apparently it is the way the airplane does work. But that was not apparent to us.
This was addressed as a recommendation in the final report:
Require Airbus operators to expand the angle-of-attack-protection envelope limitations ground-school training to inform pilots about alpha-protection mode features while in normal law that can affect the pitch response of the airplane.
Providing training on the innards of the 'good' system, is far better than taking out a vital protection. Vital because of one thing the report points out (which is in no way a disparagement of the crew):
The NTSB concludes the captain’s difficulty maintaining his intended airspeed during the final approach resulted, in part, from high workload, stress, and task saturation.
Protections are good for such high workload, stressful, and task saturated situations.