The feds can't "force" the provinces to do anything.
the Canada Health Act lists the conditions that provincial/territorial health insurance plans must respect in order to receive federal cash contributions... conditions (5) related to: public administration, accessibility, comprehensiveness, universality and portability. Again, towards CHA compliance, provinces have enacted their own legislation such as:
=> restrictions that stop a doctor who bills public medicare from charging a patient an additional amount (extra-billing);
=> restrictions that prevent physicians from billing both the public and private systems simultaneously, at least for “medically necessary” care (dual practice);
=> restrictions on physicians in the private sector charging prices for medically necessary care that are higher than those permitted in the public plan; and
=> restrictions on private health insurance for services that are covered by medicare.
and you're wrong if you belief the CHA legislation/law has no impact upon the provinces - it's exactly why current private clinics don't charge greater than what's allowed for insured services.