Someone putting up a bunch of words doesn't bind you to a contract with respect to scraping or anything else. (At most they can give up a right. They can put something in the public domain, for example, by giving up their copyright.)
To give some extreme examples: What if the site says you owe them a million dollars if you even look at the site? What if someone put a sign on their lawn that says anyone stepping on the grass can be legally shot? Are you OK with those just because they said so?
Scraping is copying, which is an exclusive privilege of the copyright owner under copyright. In the absence of a license or a copyright exception, you have no legal right to exercise that privilege. Someone putting words on a page might give you a license for the use you intend.
You don't need to be bound to a contract, because this isn't about restricting a right you have in the absence of license.
Is it necessarily copying in a sense that is different from how a web browser acquires the resource to render it? For example, scraping data to derive some non-protected facts could be considered consumption in the same sense a human reading it via a client would, and doesn't require storing a copy any more permanently than a browser.
Intent is probably a lot more important, legally, than the fact that you are technically copying something simply by "accessing" it in a browser. If you are scraping with the intent to extract and copy the copyright protected content, sure, that's a good point, but that's by no means the only use of scraping.
Personally, and I understand that this isn't how it works legally, I think that the contract is implied by the protocol. I request copies of information by means of HTTP. If the distributor doesn't want me to have a copy, they can choose not to respond with a copy. I never make a copy in that case: the server is, hence I have not reproduced the work. It's not me taking a book to a photocopier, it's me calling the publisher and asking them to send me a copy of page 237.
It's different in purpose of not mechanism, and insofar as there is an implicit license to copy in a browser for display, it is another step to establish that such a license extends to other purposes even if the mechanism is the same.
Also not that the existence and scope of implied license can be affected by the presence and terms of an explicit license, which is one reason you might want to read the T&C prior to scraping.
Also, the validity of a set of T&C that I didn't explicitly agree to and likely never read is dubious, inconsistently enforcable at best.
No, I'm not. Fair use is one (of several) copyright exceptions and, as such, is addressed in my post.
Google won't bombard your site with requests and at worst will cache data but not try to make use of it.
This is changing, though, with Google's slow but steady movement of organic search results down the fold.