The late withdrawing student

The Philosophy Smoker has a lively discussion of students' seeking late withdrawals from classes under circumstances like these:

This has happened at least once a semester since I took this job. A student who has been underperforming all semester--turning in half-assed homework assignments, missing a lot of class, earning failing grades on exams--realizes suddenly that he or she is going to fail the class. But it's after the late withdrawal deadline, so there's no simple way to get out of it. So they write me an email or come to my office and ask me to give them permission to obtain a late withdrawal.

An anonymous commenter (6:50) makes a forceful ethical argument against granting these withdrawal requests:

when you grant these requests, you aren't simply doing them a favor. You are going on record as vouching for their having a reason that the University considers sufficiently extenuating. If you just grant it to make their lives easier, *you are lying*. You are also misleading people at other schools to which this student might transfer, etc. grades convey information, notably about the amount of effort a student put into a class, even if they do so in a broad way only. And so on. Your job is to teach people, part of which involves having the grades students receive at least somewhat accurately reflect the performance of students in your class. A student might ask nicely to have you change a C to an A, because then they could get into a better grad school. But it is, basically, wrong to do so. It constitutes an act of deception on your part. The fact that such deception benefits a student is beside the point.

I confess I don't deal with late withdrawal requests like these often (perhaps a byproduct of a quarter system?), but I think Mr. Zero's attitude is the right one: Allowing late withdrawals for 'extenuating circumstances' (illness, family problems, etc.) is reasonable, but letting failing students do this sends the wrong message to them, lets them take up precious class slots, and puts the faculty member in the awkward position of having to attest to the legitimacy of the student's excuse.

So I say 'no'. What say you?