"There is one ledger"
Is untrue if (as it appears) you are referring to the side chain and Bitcoin, and true only if you are referring only to Bitcoin.
Each side chain has its own ledger, its own block chain.
Understanding side chains is much easier than understanding your descriptions of them.
"There is one ledger to rule them all" is, I believe, the correct statement. Yes, sidechains create sub-ledgers but their scarcity is dependent upon Bitcoin's