Isn't it a bit more complicated than that though? While you certainly aren't entitled to republish things, you (ie anyone and everyone) have traditionally been free to consume public material in whatever way you see fit. The precedent from the recent LinkedIn case regarding scraping supports this.
Also you focus on Google, but anyone with sufficient resources can scrape the public web (anti-bot cat and mouse games notwithstanding I suppose).
(Paywalled sites that allow Google to scrape them for search indexing purposes are an interesting edge case though.)
Even if you got an answer to your question, how would it affect the the parents assertion?
Should the internet provider of the person reading the blog post get royalties for the book the person wrote? Should you be paid for your snarky question, as the generator of content?
If you break the distribution model of content producers there won't be any new content, and the old content will simply rot away.
Radio broke the distribution model of record disks.
YouTube broke the distribution model of old content producers.
People still make music and more content than ever before. People are not gonna suddenly stop generating knowledge because of Wikipedia. The prediction that "there won't be any new content" is hyperbolic and just plain wrong as demonstrated by history.
The interesting point here is: can a non-free site let Google crawl it in order to be searchable, while not allowing them to exploit their content otherwise?
I don't see any legal ground for such a limitation, so I can't imagine what would e.g. eBay or Walmart put in their suit if they tried to put such a limitation and then saw Google not honor it. Maybe someone with a legal background could comment.