A channel gets funded when it gets opened, so it makes sense to be opened by the person who has to pay the other person.
Yeah, that makes sense.
Correct. But as a customer buying groceries, that should be fine. If you're a supplier selling something to the store it's a different story.
In that scenario, they would have to be the the ones who open and fund the channel since they are paying and sending me Bitcoin.
You lost me here. How do I establish the connection to the grocery store in this scenario? I send LN payments to the node operator. The node operator opens a channel to the grocery store?