Anyone who puts anything on the web is at the same risk. For example, ask Google how old Queen Elizabeth is [1]. Google tells you the answer in a big font at the top of the result page. Google sourced the answer apparently from usnews.com but you didn't even have to click the usnews link. Google "took" the answer from them and deprived that website of a click.
So yeah, you are donating your work to Google when you put it on a publicly accessible web site.
If all of the useful information in a web page is mined and given away by a third party in an automated fashion, such that the copyright holder is deprived of revenue, then that's not the intention of 'right to quote'.
I'm pretty sure Google pays these types of content publishers (like Reuters) very handsomely. In this case, the content distributor (USNews) also went out of their way to SEO their site with microdata[1], so I'm going to guess a lot of their inbound traffic also comes from Google searches.
So yeah, you are donating your work to Google when you put it on a publicly accessible web site.
[1] https://www.google.com/search?q=how+old+is+queen+elizabeth