If I give someone an account on our BTCPay server and they attach their own wallet to it will the lightning payments they get also go through their own wallet or will it be using our node for the lightning payments?

And if it does will that still count as not having a middleman apart from the lightning network?

I am asking because we are not fully peer to peer right now since we are using our own account to make the beta fundraising pages. BTCPay Server makes it easy to do these fundraising pages and to have payment processing without paying a third party but I am wondering if it is technically speaking still peer to peer charity as we want to advertise. If not then we would have to build our own system to replace the functions we use it for.

Appreciate any opinions and suggestions.