It's reputation precedes it. I am here in Canada and I attended a Tech/Business summit few weeks ago in Saskatoon and there were people from all over Canada there. UCW, Crandall and Ambrose university were particularly mentioned in discussions as employers tend to avoid graduates from there - not because they are private, but because of lack of quality.
I know people go the study route for the ultimate goal of getting a PR, but to that, after you've completed your program you will need a long term job in the professional NOC to pursue a PR application. If employers won't hire you, you will have a hard time meeting that requirements.
Also, as mentioned above, VOs knows that this school accepts every Tom, Dick and Harry and that their admissions requirements are not as stringent, therefore they will most likely be attended by students who do not genuinely want to study. Hence, the higher refusal rates we see for private universities and colleges in general.
Like you said, if you opt for a private DLI, you'll need a lot of luck to accompany your application.