The native token is not the same as a token with parity to the native token. The main difference, as I already said, is that layer 2 inherits the security of the main chain, while side chains do not, since they have their own rules and consensus protocols.
It is not the exact same thing but it IS the same asset which is opposed to the asset being some other asset. This would effectively break the tie to bitcoin and make said chain a layer one if the native asset were different entirely.