Yes, I think it can. The conversation about privacy always gets blurry, but there is a truth that the sentence "x is private" is kind of meaningless (or perhaps just untrue).

We should be asking private from who?

Custodians provide excellent privacy from everyone by them (or not if they leak your details).

It's entirely possible that monero is better at hiding your identifying details when you send while lightning is better at it when you receive.

I'm glad super is poking these assumptions.