It's very possible I'm misunderstanding as well, but when you create a room on the Matrix homeserver, the only option you have is to make it so users on another homeserver cannot join that room, which means your only security is other matrix users not knowing your room name.

For a small corporate team that wants to pilot a chat program, like in the original comment, the gulf between Slack setting up your own private workspace with a few clicks and a room that has all of your chat history exposed to any user that knows the room name is pretty large.

I would love to see riot or matrix give you a few click options to have them host your own private matrix server, as that's a big obstacle for corporate customers who don't have the resources (human) to spin up their own servers (domains, adding ssl certs, adding nginx, etc.) just for trialing a chat program.

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.

Great, thank you very much for clarifying!