I don't think Mex is lying.
Or that the story about private insurer not paying directly to hospital is a lie, either. Canadian Medicare - MSP - covers you out of country, though coverage is very low. So when you buy private insurance, the Primary Provider is MSP. If insurance company has no agreement with MSP (many companies don't), then you pay FULL AMOUNT out of pocket and later file a claim.
The fact that MSP will stop after 6-7 months of absence you can verify in govt documents. You "might" sneak in and out of Canada without them noticing, but if they catch you, the stakes are too high. This is why Canadians in Mexico are mostly snowbirds, going back every 6 months.