Lower tuition = Better access for the Poor?

I'm baffled by the logic of countless student groups who proclaim their desire to reduce tuition fees so as "increase access to education" for the poor.

In lowering tuition rates across the board, they are effectively promoting the subsidization of education for the rich, and often for themselves. Altruism concealing selfishness.

If you truly want to increase access for the poor, the last thing you do is lower tuition rates. In fact, raise them.
Afterwards, you use those additional funds from those who CAN AFFORD to pay to provide bursaries and grants for those who can't.

And it worries me that so many of my fellow students are aspiring "leaders of tomorrow", yet so often devoid of basic logic.