In a nutshell, the Canada Health Act, states that any "medically necessary care" will be provided through public funds. If a province allows private clinics to provide "medically necessary care" for profit then the transfer funds from the federal to provincial governments will be cut by that amount. Eg. people pay a total of 500,00 for private care then the public purse is cut by that amount.
The debate is what constitutes a violation of the Canada Health Act. Enforcement is also variable and subject to the reigning government's belief on private pay care. The report details which clinics exist, which "violate" the act and how they "violate" it.
The CHC also draws conclusions about the impact private care has on health care personnel supply and wait times. They've concluded that it adversely affects both. From a purely scientific point of view, I found the study design of low quality* (anonymous phone survey) and highly biased so I think they've over-reached with their conclusions. I think private clinics have been in existence for too short a time and in too limited a capacity to draw any real conclusions about wait times or their impact on personnel. We could also look to a mixed system such as the UK to get a better assessment of the impact.
That being said, it is a reasonable cross sectional survey of the current situation in Canada and worth a read.
*the asked the front desk person how the clinic used public pay systems. "do I need to bring my medicare card", etc... while biased they also write the text of the coversation so the reader can judge for themselves if the conclusions are warranted.