Seems like you're assuming a placement agency has to be involved to get a job offer as a foreign worker. Nothing could be further from the truth.
People get jobs and approved LMIAs without going through placement agencies all of the time. They do this by applying to roles with companies directly. If the company has found the role to be difficult to fill from the Canadian talent pool, there's always a chance the LMIA will be approved and they may be willing to go through the process.
Again, any placement agency asking for money in exchange for a job in Canada should not be trusted and is most likely a scam. Apply for jobs with companies directly.