But how would a sidechain token not be pegged to Bitcoin? To receive some tokens from a sidechain, you have to back it up with your Bitcoins.
A sidechain token would be pegged to
some value denominated in BTC, yes. Either way, the market shouldn't value them equally because sidechains are theoretically much less secure than Bitcoin.
Plus the sidechain is not a separate network, it is still Bitcoin.
That is definitely false, and it's a dangerous assumption. Sidechain tokens are not compatible with the Bitcoin network; you cannot send them on the Bitcoin blockchain. They operate under a different set of consensus rules.
And they are insecure. Under no stretch of the imagination are they "Bitcoin."
The alternative is that all Bitcoin nodes and miners fully validate a given "sidechain". But then it ceases to be a sidechain; it's simply part of the mainchain consensus. That's the ultimate problem with sidechains: by definition, they are
always less secure than the mainchain.
A better way to think of sidechains is parallel to the idea of cross-chain atomic swaps on two separate blockchains. There are too many theoretical situations where your locked mainchain funds could be stolen by dishonest miners or via trusted setup to consider these networks "Bitcoin." They don't offer Bitcoin's security, not even close!
They are altcoins that can communicate with the Bitcoin protocol.