[rdiddly]

But this is about an arbitrary distinction between two groups of non-paying customers!

However I dispute the "customer" analogy too. In fact, turning this tired and one-sided analogy of a "store" on its head, how about it's my browser, and while they're in it, they can play by my rules?

There is nothing about a client-server paradigm (especially nowadays with thick clients) causing me to be "in their premises" or causing that to be a better analogy than their being in my premises[1]. The "online store" was just an analogy, and was how the www was sold to millions of profiteering dullards starting in the 90s, so naturally the idea has gotten a lot of traction and you can be forgiven for still thinking of it that way.

[1]Neither is accurate of course - The truth of the matter is that my robot handshakes with their robot across space. (And then their robot asks the Twitter robot whether my robot has the special Twitter street cred badge.)