Is false. Google is big, but even they couldn't handle the load of a large fraction of the world's web browsers sending them a request for every page loaded. That'd be insane.
Google Safe Browsing is based on a Bloom filter. The browser downloads the filter in a series of requests when it first starts up, or when the filter is out of date. It also sends a followup request if it finds a hit, but this is rare unless you're actually about to visit a site that's been flagged as unsafe.
> It also sends a followup request if it finds a hit, but this is rare unless you're actually about to visit a site that's been flagged as unsafe
And the followup still doesn't send the URL or even a hash of the URL. It sends just a prefix of the hash to download all URL hashes matching that prefix to do the comparison to the actual current URL locally.