Canada requires you to (re)enter under your newly granted status in some circumstances, but that is entirely different from requiring you to leave the country before you can apply for a change of status, and to remain outside of the country while the application is processed. I was free to come and go from Canada as a temporary visitor while I waited to get my PR, and I had the option of applying from within the country as a non resident as well, with some caveats.
Think my European buddy had to go back home to renew his work permit. Could not do that within Canada.