Nothing you quoted contradicts what I said.
Some reading for you on the subject:
The PBO’s annual long-term fiscal sustainability report released Thursday says the Harper government’s decision to scale back the growth in Canada Health Transfer payments means provincial governments will increasingly struggle to afford health-care services for their citizens.
“Far from putting our fiscal house in order, this report shows how Conservative cuts to the Canada Health Transfer and Old Age Security are actually just downloaded these costs onto the provinces and individual Canadians.”
https://nationalpost.com/news/politics/ottawas-overhaul-of-health-care-funding-has-left-enormous-fiscal-gap-for-provinces-pbo-warns