The question type that uses this facility is the file upload question type that Adrianne Boyd wrote as part of last GSoC. (http://moodle.org/mod/data/view.php?d=13&rid=976)
However, this is a often-requested feature for the Essay question type, so my thinking is that now we have Adrianne's code as a proof of concept, I will actually add this functionality to the essay question type for 2.0 (as an option that the teacher can turn on).
I think the logic with the capabilities is that the file is part of the student's response. mod/quiz:viewreports lets you see student responses, so people with that capability should be able to see the files.
I have checked in the code for this.
Petr, I would be really grateful if you could review it, particularly from a security point of view. Thanks.