Quite frankly, Russian hospitals (including the "good" ones) are crap and everybody who can afford it goes out of the country for any medical care - Putin could afford it, but clearly can't afford to leave.
He can bring in doctors and some equipment for something simple, but he can't bring in a state-on-the-art oncology clinic.
Russians go to the UK for dental care - and that is saying a lot (sorry Golfy...)