Sites will not get hit for grammar, per se - at least not at the moment. But what can already happen is monitoring visitor behaviour.
So, a visitor hits a page, sees that the article is badly written, does not answer her question, is unattractive to look at she will click away. This is not a particularly new thing.
Increasingly SEs will not present material to searchers that has been rejected by other searchers. A couple of years ago that meant that webmasters started to look at decreasing bounce rates, increasing time spent on a page and then site and one of the beat ways, was and is, to provide content that people want to read.
One of the best indicators of material that people will read is grammar and syntax. I KNOW as a reviewer for my own sites that a badly written article will almost never have decent information. The people who provide content worth reading take care to ensure it reads well. So, whilst Google may not be grammar checking, it makes perfect sense for anyone interested in having content worth reading to ensure decent usage of the written word.
Let me ask you what purposes you think a link has.
Please let us know, when you say that you use other people's websites to host your content, what is a backlink for?