What's the etymology of English letter casing terminology?

The popular consensus around the web (i.e., Wikipedia) seems to be that "upper case" and "lower case" originate from typesetting convention of upper and lower drawers for letters, possibly preceded by the Latin terminology of majuscule and minuscule.

However, none of these references seem to be backed up properly, and frankly, I find the explanation tickling my urban legend senses - my suspicion is that this is an incomplete or even false etymology, but I can't find anything better.

Is there a more authoritative source that attests to whether or not this is a true etymology?

Solution 1:

The full OED explanation is that in printing a case is ‘The receptacle or frame in which the compositor has his types, divided into compartments for the various letters, figures, and spaces. In ordinary printing the compositor has two such cases before him on a slanting stand, the upper case containing the capitals, etc., the lower the small letters, ordinary spaces, etc.’

This is supported by four citations, the earliest dating from 1588.