> End receiver has to share that invoice though I assume?
It's not strictly necessary. You could use a keysend payment to pay a group of nodes atomically without getting an invoice from the recipient. But if you *do* get an invoice from the recipient, that doesn't mean you are trusting him.
The invoice need not contain a list, created by the end node, of the people to pay. It *could* contain such a list, since ln invoices support custom fields; but it could also just be an ordinary ln invoice, and the sender could choose what additional nodes to pay through some out-of-band method.
The point is, LN routing works by atomically splitting a large amount into small sums which are dropped off node by node, atomically, and this can be turned into a payment splitting function by rendering each payment as just a large routing fee. But it has some drawbacks, like not working well if a recipient does not run a routing node.
