No, this is the rhetoric that one political side pushes because it's convenient. Meanwhile the data shows almost all the housing is owned by either Canadian citizens or corporations. It also shows Canada will rely exclusively on immigrants for population growth by 2030 - it would end up with an aging population and no one to pay the taxes supporting pensions if they didn't. Most of Vancouver is zoned for single/dual families only so it's impossible to construct more housing. Of course prices rise when they don't let supply rise to match demand
You can become a canadian citizen 3 years after getting your PR, usually. It would make sense for high earners to wait a few years before buying, and by that time they are already citizens. I might be completely wrong, but I just don't see how citizenship of the owners really disprove anything.
Sure, immigrants initially rent. That puts a massive upward pressure on rents, which in turn increases housing value. It’s so easy to become a Canadian citizen that when these folks do buy they’re citizens in just a few years.