> it'll deliver the encrypted blob to the client, so in theory if they really wanted to break your password they could tell the extension that it's encrypted with a single round of the hash function

That's incorrect. When you change the round count your master password is re-computed, and database is re-encrypted with the new hash. The server needs to return the round count so the client can generate the correct master password hash, if you ignore that and simply calculate it for e.g. 2 rounds, the master password hash won't match and therefore the AES-256 database won't decrypt.

The way Lastpass works is straightforward... PBKDF2(password, rounds) -> AES256(hash, blob). If the rounds change then the resulting hash changes and therefore the database won't decrypt. Your second paragraph is quite confusing, in that I cannot make heads or tails of why you think you can use 2 rounds when e.g. 10,000 are specified previously. A correct round count is just as vital as a correct password in generating the correct hash.