I think the way it works is, the unit of account offchain is equivalent to the unit of account on L1 if the user can always unilaterally force it back to L1. "bitcoin" is bitcoin in a payment channel or virgin VTXO that the user personally owns. L-BTC and cashu sats are not bitcoin since those systems don't provide unilateral exit. the guarantee of unilateral exit must also be furnished entirely by the consensus rules of the L1 itself, with no dependence on third parties.