For the public observer, yes. But always consider that we, Boltz, do have the association.

The exposure is that we might be forced by law enforcement to reveal the association between two payments of a swap. This didn't happen so far and we expect El Salvador authorities to only require this for serious crime, but it might in future and we'll have to comply, see https://boltz.exchange/privacy.

That all being said, sending Lightning to Boltz provides very decent privacy and we don't have a way to tell where a payment came from. That's the sender privacy part. With Bolt12 and blinded paths receiver privacy on LIghtning is getting a massive boost too and we are working together with the team at Breez to ship something very soon that makes Boltz fully Bolt12 compatible. Here the main PR that was merged just 3 days ago: https://github.com/BoltzExchange/boltz-backend/pull/859

Tl;dr: using Lightning is a very good idea as it doesn't reveal origin and with Bolt12 blinded paths neither destination to us and thus there is nothing much to reveal in the first place ✌️