The situation as I read it is private clinics are charging the provinces for services covered by Medicare and are charging patients a surcharge for these services.  So either services at private clinics cost more to do the same thing or the clinics are " double dipping" or clinics charge patients for the chance to " jump the line" by paying extra for a service.
Funding for health care is Federal, but decisions for health care spending is Provincial.  There was instances revealed recently of provinces allocating  health care funds to general revenue, so there is some murky stuff going on here.
In Manitoba, for instance, our government hasn't even signed a health care contract with Ottawa yet, and is closing emergency wards and Urgent Care wards. It seems to me the problem here is more complicated that simply underfunding from Ottawa.  In Manitoba, for instance, there have been cases of blatant double billing by clinics that are now criminal investigations.