Rusty said similarly on IRC, and I understand that. But here is something that I dont understand.

If I make a transaction on a payment channel, following all the Script rules, then how does channel funding play a role?

I assumed that funding a channel via op_cltv and op_csv were required only to setup the channel, and thus whatever transaction took place would be "outside" the scope of Script and rely on different rulesets.

If Script is still in use, it implies that all transactions are subsequently recorded in mempool as they are Bitcoin transaction, but with the only exception of that they wont get mined (due to op_cltv/op_csv settings). This sounds, wrong, so I am sure I missed something in terms of the transaction abstraction on secondary layers.