As far as I can tell, those servers are just a convenient way for your own node to communicate with the network. It doesn't appear that the user is using on of their nodes. I don't see how that translates to Mutiny having custody. All they seem to be doing is offering a server for convenience. Of course setting up your own server is more complicated, but that doesn't mean you don't custody the funds.

What am I missing?

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Yes, you control the keys of that node. But only that.

If the domain / server where it reside the whole software, goes busted or just shut down, you practically have the funds blocked, until you do a complex recovery.

That is not a real "self-custody". Is just partial.

Is better to inform well users and do not lie to them with fancy words just to gather more users.

The phone or whatever is running the full node. Mutiny is simply setting it up for you and providing a communication server if you want to use it. That isn't the same thing as Mutiny running the node on their own servers.