an old meme, and my usual recommendation: just test it: create a page that i not linked from anywhere. visit it with the browsers mentioned above. watch the logfiles. wait for it. nope, no googlebot request. it is unbelievable easy to test, i have done so on various occasions in the past, so there is no need for you to spread a "several people have reported" rumor. just ... test ... it.

as for the old stories, that google does this kind of thing: people, especially SEOs or people who think they know SEO, always blame google. oh, my beta.site has been indexed, it must be because of ... google is evil.

most of the times i have seen cases where googlebot found a not published yet site it was because of (just some examples, not a complete list) i.e.:

* turned on error reporting (most of the PHP sites) * the URLs were already used in some javascript * server side analytics software, open to the public * apaches shows file/order structure * indexable logfiles * people linked to the site * somebody tweeted about it * site was covered on techcrunch (yes, really) * all visited URLs in the network were tracked by a firewall, the firewall published a log on an internal server, the internal server was reachable from the outside * internal wiki is indexable * intranet is indexable * concept paper is indexable

testing your hypothesis "chrome/google toolbar/... push URLs into the googlebot discovery queue, which leads to googlebot visits" is easily testable. no need to spread rumors. setup for testing this: make an html-page (30 seconds max, basically ssh to your server, create a file, write some html), tail & grep logfiles (30 sec max), wait (forever)