Disrupting Innovation

I think it is important to evaluate this feature in terms of what it offers to users, rather than what it offers to Google. The user may save time by not having to go to Amazon.com first, but does Google site search provide a superior search experience for Amazon and every other site for which they offer this UI?

In my case I often search on amazon.co.uk and I have to admit their search is near useless. It doesn't seem to handle synonyms, or misspellings and sometimes you have to tell it which corpus to search if you want to get results. Amazon search is slow and has a very clumsy interface, compared to Google. If you already have a navigational subpage in mind, the Amazon search experience will take longer and probably distract you. This may be fine for Amazon if you get distracted and browse around their site for a while they make more money. But many users want a way to hop directly to the page they're interested in.
The search box saves the user a click. Won't a good search engine reduce a user's browsing time normally?

On the other side it is important to remember that some of these websites rely on users browsing their pages and they make money that way. This feature seems to be pretty arrogant: Google assumes can search their own site better then them, and that user's search experience of the website via Google search is better, which in some cases is far far from the truth. It is crucial to notice that Google offers an opt-out option for those who do not want it, so it is not so evil.

But when does the secondary search box appears ?
If you read the official blogpost, it explains that Google is only showing it on searches where it would be useful.

. Like the rest of our snippets, the sites that display the site search box are chosen algorithmically based on metrics that measure how useful the search box is to users.

That is, it's only appearing when people are already searching for a domain, and then modifying that domain to add some specific terms.
It seems fair to me. What do you think ?