> the same math that allows a javascript library running in a web browser to extract the private key being computed in a VM elsewhere on the machine

I am not entirely certain whether I was clear about the point I made in my message, however I have asked a very specific technical question and you are making some generalised sweeping statement about privacy in the most widely used case.

We could not decrypt any ancient languages, for example; if we didn’t have an equivalent of a Rosetta Stone for them. Thus you should not be able to do the same for the encrypted database I assume.