The chrome extension could automate the "root" verification this way:
When the extension discovers a blind liability proof, request http://verificationserver.com/?root=. The verificationserver can then independently fetch the root file and send it back to the extension. The extension can then verify that the retrieved root matches the partial tree's root.
The 3rd party server is necessary to avoid a malicious site from sending a custom root file to different users.
Moved to olalonde/solvency-verifier-extension#9