Mutiny is awesome and probably the best thing in bitcoin for the past three years, BUT it is not quite 100% self custody. It's more like 96% self custody. When you receive a payment, they open a just-in-time channel to you and push an amount to you that is equivalent to whatever the sender originally sent, minus a fee. In return, your browser immediately gives the preimage to the payment hash of your original invoice, allowing Mutiny to settle the payment from the sender.

By giving them the preimage, however, you're giving them custody of that money, at least until the just-in-time channel confirms. The reason is because the money in the channel contains your payment, and Mutiny can easily take that money back, while still keeping the money the sender meant to go to you. All they need to do is double-spend the utxo that went into the channel and return it to themselves. Which is very easy because unconfirmed payments are cancelable.

As a result, whenever you receive a payment that causes Mutiny to open a channel to you, they have custody of that money. Typically this is only for a brief period of time, i.e. until the channel confirms, but that means (1) it's not 100% self custody and (2) it's not necessarily "for a brief period of time." How long they have custody of your money for is completely up to them. You do not have control over that and there's nothing you can do to stop them from keeping your money indefinitely -- forever, even.

So yeah -- mutiny is awesome, and it's even 96% self custody. But it's not 100% -- not yet -- and I think that's important to point out. Appreciation for these guys and what they are doing is great but their product is only nearly perfect. (I estimate about 96% perfect. Which is awesome! Like, jump-off-the-walls awesome! It's so cool and mesmerizing I am flabbergasted by the implications! But it's not quite perfect. Not yet.)