I've read it a dozen times already so, no, I know how this stuff works.
http://www.blockstream.com/sidechains.pdfYou will notice that there is not ONE mention of
Bitcoin or
transaction capacity
scaling inside.


I'll admit I was wrong. How'd I miss this

Anyway the point still stand and I think it is fair to say no one ever proposed sidechains would allow us to support a significant increase in transaction. In the quote from Hill referred above "scale" was used pretty liberally and it is clear his more important message was "faster transaction processing".
From the same article:
Gregory Maxwell, who first proposed two-way pegging, says that it could provide some relief for bitcoin, though:
"I don't think this will remove the need to increase bitcoin's throughput entirely, but if the technology matures fast enough it may allow for a more conservative approach that increases size only when its very clearly safe to do so."