More om medical healing:
The Medical Magic is one branch of magic that helps to cure and treat magical injuries and diseases. Wizard medicine is well ahead of its Muggle counterpart. While Muggle medicine largely attempts to stimulate the body's own healing and defence systems, magic can simply impose well-being. Healing is not as simple as ordinary spells, but should be able to cure minor injuries in a negligible amount of time and just about every other problem (even missing or boneless limbs) given somewhat longer. Conventional ailments, save from large-scale neurological damage, appear to be very easy to fix. Of course, a number of problems in a setting like this do not qualify under conventional ailments. Despite their advanced medical "technology", wizards apparently cannot use magic to cure minor inherent conditions such as myopia.
Wizards had a cure for the common cold for years: it is known as Pepperup Potion and is characterised by the patient emitting steam from their ears.
Wizards do not appear to make use of vaccinations, however: a common cause of death appears to be dragon pox.
Wizard doctors are known as Healers and Mediwizards. While Madam Poppy Pomfrey runs a hospital wing at Hogwarts, the central establishment, in England, for this purpose is the St Mungo's Hospital for Magical Maladies and Injuries.
As Madam Poppy Pomfrey is said to be a matron, there may be different ranks of nurses like there is in the Muggle world. For example: Matron, Sister, Staff Nurse, Nurse, and Student Nurse
Various magical diseases, such as "dragon pox", "spattergroit" and "Vanishing Sickness," are treated in St Mungo's. Wizards tend to view Muggle medicine as primitive and barbaric.
There seem to be a couple of limitations to medical healing which scientific medicine has no problem whatsoever with.
My analysis of the way medical magic work is that it revolves a lot around what's natural and not. Like, they cannot correct any "problems" you've been born with whereas they can repair broken arms like it's a cough. Another guess of mine is that they cannot repair damages that require the creation of a something that is not already a part of what is in need of repair.
Such as, you can repair a broken arm, even removing the bones in the process and grow new ones, but you cannot create a whole arm from scratch. You can repair entities such as "arm", "eye" and more but you cannot create these where they've been lost.
I'm basing this completely on Moody not having a foot and an eye, though if he lost those body parts due to a magical wound I guess that would invalidate this hypothesis.
But let's assume this is the case, medical magic cannot create but rather mend and repair (which I believe seem to be the case in other areas of magic, food apparently cannot be created from scratch but once you have food you can create more out of it).
What happens when you get radiation poisoning then?
The radiation will begin to destroy the cells in the body that divide rapidly. These including blood, GI tract, reproductive and hair cells, and harms their DNA and RNA of surviving cells.
Basically, the harm has already been done. It's not an ongoing "poisoning" per se but rather you just have an ongoing display of symptoms of an event that have already occurred and left it's marks on the body.
The cells in your body has been altered and you're now experiencing the effects of this, your body is slowly ticking towards death and all you can do is try to help your cells and prolong your life.
Now, that the damage is on a cellular level shouldn't pose a problem for medical healing - magic doesn't concern itself with details.
But I could see how a change of something that makes it look "natural" which I've interpreted as being a state. Your new radiated body is the new state of your body, while it's a damaged version of your old body it's not something that on it's own, through natural means, will ever return to your original state.
Thus the new radiated body is what is "natural", which means that they cannot heal it.