I think the notion that there is one main ledger is absolutely accurate
In my view, the more accurate definition of sidechains are that they are a sub-ledgers of Bitcoin.
I would mention that in certain fairly important ways, the transparency of the open blockchain is more of a bug than a feature when it comes to free use of the currency. Aside from the obvious privacy issues it also cracks the door more than a little for such things as 'red-listing'.
In other ways it is absolutely a feature, and the one which is primarily responsible for the confidence that one may have in the system integrity. So it, like so many things, is a mixed bag.
Point is that sidechains have the potential to favor and disfavor the pros and cons of this transparency depending on their individual goals. To the extent that some sidechains will almost certainly put some focus on privacy it will make it significantly more difficult to perform privacy-quashing analysis in the Bitcoin masterchain.