it is not true. You can't apply just by being here. You have to meet a few criterias to qualify, you need to have studied in Quebec in a designated instituion and the course has to be at least of 800 hours. Another option is being a temporary worker, after 1 year of work experience you are then qualified and can apply.
These are the options I am aware of. Certainly being only a visitor won't allow you to apply anytime. Not sure, but I don't think that paper based still exist. I don't think so. I guess all applications are done via Mon Projet now.
Regards.