The guy making said claim is an idiot, and I'll offer evidence to prove it.
I think you are being needlessly hostile; let me offer another view of what he says.
I don't think the OP is right in its analysis, but I think where it goes wrong is in proposing just two, rather crude categories. As you say, there is no clear way of distinguishing workstations from servers; on the other hand, the idea is not without merits - there is a smallish number of typical use-categories that most computers would fit into, and which could be a good starting point for an installaion; eg. workstation, game-station, database server, etc.
It would probably not make a lot of sense to make such a large number of specialised distributions, but it isn't impossible, or even difficult, to implement the concept. Take my favourite distro, Debian: you install a minimal system, and then you use an installer to download new packages and their dependencies according to your needs and preferences. Some of these packages are 'meta-packages' - like KDE, which is not a real package in itself, but has been defined to depend on a large number of application-packages that are typical for the KDE desktop; so, by selecting the kde package, you select all the aplications that are useful in the KDE environment, in effect. It would be very easy to create other meta-packages that define other typical sets of functionality - one could even call them things like 'work station', 'server', etc if one likes.
I think what would make this process better would be if users could easily define these meta-packages before installation and then select them from the installation menu. This would address both the concerns of the OP as well as the points you raise.