Uh, you don't really "allow" them to visit your website. All you can do is disallow them from visiting by blocking them using robots.txt. If you don't have a robots.txt stating otherwise they will crawl and index your site.
UPDATE: I suppose if you specifically allow the Googlebot via robots.txt, then in that case they could probably argue that you gave them permission to access the site.
If you put a website on the internet, you are granting anyone or anything permission to look at it by default. The alternative seems obviously untenable.
Exactly, and this is why the TOS mentioned in the comment is absurd. Basically that means that if the TOS is legally valid, then technically Google can force any arbitary terms on you if you simply put a website on the internet. This would be the same as saying that all citizens of America are subject to this agreement, whether if they've seen it or not.
This is worse than shrinkwrap agreements and TOS banners at the bottom of a website, since for those you could at least argue that the person who opened the box/visited the site saw the agreement. But in this case, there is absolutely nothing to indicate that the person who created the website even knew that Google as an entity existed.
That article is about a tech-illiterate governor using his station to threaten prosecution of the press... for discussing a 10-yr old bug that's already well known publicly.
If anything, that's more to the discussion of giving social security numbers to inept IT departments.
When you put a website live on the internet, you're giving everyone permission to access it, including Google, unless you state otherwise. (Or put processes in place to make it non-public.)
UPDATE: I suppose if you specifically allow the Googlebot via robots.txt, then in that case they could probably argue that you gave them permission to access the site.