I have searched, but haven't yet been able to find, an authoritative documentation of the filesystem hierarchy of the Android OS.
Can someone tell me whether this exists at all and if so, where?
There's a big chapter on that in Andrew Hoog's Android Forensics book on that (see this Amazon list for available copies). Unfortunately, that book doesn't come for free (but from Elsevier; so prices range from ~USD 20 for the Kindle edition to ~USD 50 for the print, with some crazy offers for ~USD 170+ as well), but it explains a lot of background not only interesting for Forensik specialists. A German version of this book now is available for EUR 35, published by Franzis (which can be found e.g. on its German Amazon page as well as on the publishers site, see this link).
While the link to AndroidUserland given in a comment on the question contains a very rudimentary list, a better (though also incomplete) documentation can be found at robotz.com. As said, this is far from being complete, but better for understanding.
I remember having seen another documentation at android.com -- some hints can be found there e.g. in the Storage Options (check "Internal Storage" and "External Storage" here). But a complete documentation of the file system hierarchy is missing here as well.
So again, the most complete documentation known to me is Hoog's Forensics book. German speakers might also be interested in taking a look into the chapter Dateisysteme und Datenstrukturen of my book "Die Androiden-Toolbox", which (in this community edition) is freely available in HTML, MobiPocket and PDF versions here on my eBook Server (if you prefer a printed copy with a few more details, the (extended) Franzis edition Das inoffizielle Android-Systemhandbuch will be available end of this month, i.e. starting around the 26.11.2012).
Disclosure: As said, I'm the author of the second book mentioned. And, not yet mentioned, the translator for the German version of Andrew Hoog's book. But that does not mean I hold back other sources here, of course.