No.
Most of them come from very wealthy families, at least rich enough to pay them the best education.
You don't become poor because you're lazy. You become poor because you were born poor AND you don't have enough will, work, education and luck to become rich.
IMO, the education must be 100% free, up to the University level. In addition to that, the students must get reimbursement for their conveyance and food/stationary expenses. This will help the poor people to grab more opportunities.
It seems to me that education and not only it may not be free. I do believe that everything that comes for free it is not valued. Another thing is that it should be paid from different sources, and perhaps a loan.