In a way this can happen (though i'm far from being sure it actually does...): the medical area is one where the prices are the most regulated. In the public sector the prices for an MRI are probably very largely fixed by the government (and more probably completely) and given that even in the private sector you need an authorization to build an MRI counting them mean the medium price will not increase too much and the public operators might have less arguments to ask the government for price increase. Of course that would maybe not destroy effects of offers and demand and I don't know which one would win in the long term. But remember that health is a very different market than commodities and trying to compare the economics of health vs. crews and bolts by using crews and bolts theory might not going to work well.

The lack of MRI is a big problem in France anyway. Regardless of the effect on prices (except maybe if they triple or something like that) having 100% more would be a lot better.