This is a sincere question: have you ever been on the other side of the hiring process before?
I have, as a tech lead for a software company. I don't know how other places do it, but there's simply not enough time in the day to read every single resume/cover letter that you get.
You post a job-ad and you're drowning in resume`s and cover letters in less than 30 minutes. I also want to say that 80-90% were under-qualified and most of them didn't even follow simple instructions in the ad.
You won't believe the amount of cover letters saying things like "I have never used Linux, but I've been working on Windows for X-XX years", when the job title was "Senior Linux Systems Administrator".
When we put requirements, we really meant them. We never inflated the requirements or asked for the impossible (28+ years experience in PHP).
Our process went kind of like this:
1) Scan cover letter quickly to weed out incoherent applications
2) Scan resume (again quickly) and look for minimum-requirements
3) If 1 and 2 were met put resume/cover letter in the "good candidates" folder
4) If "inbox" is not empty, go to step one, otherwise:
5) Go back and read cover-letters/resumes in more detail
The one exception would be if something in the cover letter or resume caught our attention, we'd then read it in detail then and there.
For all I know, DropBox might have a serious need to have this position filled by a CS graduate. I doubt it, but it's a possibility. Another commenter here said something about planning to have this position evolve into something more "intense" in the future where a CS degree would be seriously needed. That's a legitimate "theory".
All I was criticizing was that the job requirements do not warrant a CS degree, and that they are probably turning away possible good/great candidates.