I wonder if Johnson rejected the USA or if it was his successor? Probably the latter. That's a factor two, not that he wants Johnson to die but let's face it, the stakes are quite a bit less for him if Johnson dies. For Johnson it's the ultimate stakes, for Raab, well he not only lives but he's de facto PM at least in the short term. So political considerations could come into play under that situation.
A few decades ago, I worked in the British NHS. Anybody who thinks they will get all the care they need because it’s Socialized Medicine, is sadly mistaken.
That being said, I suspect that Boris will get top notch care. Britain still has private healthcare (you can pay for private insurance, but it is on top of the high taxes you are already paying for everybody else’s healthcare) and get good treatment. I doubt (even if the doctors are on Labour’s political side) that they would want their PM to die while in the care of the NHS.