I understand what you are saying.  I just think it is incorrect.   

They are going to be out of dept sooner if they pay the debt in the logical order.  It's conceivable that paying it in the wrong order could produce very little gain each month, whereas paying it in the logical order might produce much more gain.

For example, suppose there is overdue credit card debt charging 20% interest.  Paying $x on that principle is going to produce a lot greater increase in paying ability next period then paying the same amount of money on a 3% student loan, even if the student loan is $1000 and the credit card debt is $20,000.  Paying principle moves you forward.  Paying interest is just kicking the can down the road. 

The fact that you are discussing this makes me pretty confident you understand it, so I'm not real sure what the point of the discussion is.