Afaict that's not technically correct. For example the GPL doesn't require that you provide the source code up-front, it's enough if you provide it when asked for. Which seems to be what the epic folks do.
2. Source Code
The program must include source code, and must allow
distribution in source code as well as compiled form.
Where some form of a product is not distributed with
source code, there must be a well-publicized means of
obtaining the source code for no more than a reasonable
reproduction cost preferably, downloading via the
Internet without charge. The source code must be the
preferred form in which a programmer would modify the
program. Deliberately obfuscated source code is not
allowed. Intermediate forms such as the output of a
preprocessor or translator are not allowed.
So it really depends on your interpretation of "well-publicized means of obtaining the source code". I don't think I would label a "send us an email and (maybe) we'll give you the source or the patches) as Open Source, mostly because if a company doesn't already have their source in the open, they don't want it in the open, doesn't matter what they write on their site.