In a very real sense, all physicians give a limited warranty – it’s called malpractice liability.
Certainly no one wants to be seen as an easy target, but in many cases a quick resolution of a patient’s unhappiness is far cheaper than the costs of a dispute; not simply those associated with a potential lawsuit, but also time, hassle, and publicity, even if the publicity is limited to the hospital C-Suite.
Last, giving an actual warranty, not of outcome but of satisfaction, with a pledge to resolve issues, serves as a competitive advantage.
If you’re already giving a de jure or de facto warranty, why not leverage it to your benefit? It’s likely that your competitors never will.