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? 

 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. 

 Bro, the node isn't on a server. It's on the user's device. 

 https://blog.shyfire.net/blog/self-hosting-mutiny-wallet
and
https://github.com/MutinyWallet/mutiny-node 

 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.