[Arathorn]

This is indeed a massive misunderstanding: rooms in Matrix can either be publicly joinable by default or be invite-only (just like in IRC). There's also a separate question of whether a room is locked to a given server (i.e. made unfederatable), but this is an extreme measure taken if you know the room will contain stuff you never want to ever leave that server. You can now also create communities to group your company/project's rooms together even if you're primarily using someone else's homeserver.

Separately: we're working on providing a "one-click" homeserver hosting option with a free trial precisely of the kind you're asking for.

[jmagoon]

Great, thank you very much for clarifying!