They do. But you sending out from the mint is what makes it private. You are simply telling the mint to make that payment for you.
Discussion
okay, that's interesting. is a mint making a lightning payment any different than another custodial lightning wallet service?
to me, I have been thinking that one of the greatest advantages to ecash is that it solves the "no path" failures typical of lightning.
ecash sent between Alice and Bob, both members of the same mint, doesn't even touch ln network right?