There is so much misinformation on this thread and generally on BHW about this concept. Anyone who says Google can decide if an article is "well-written" or not has no idea what he is talking about. Please take some damn lessons in programming first and artificial intelligence. You need to understand there are 2 major cases: manual action and algorithmic one.
With manual action, HUMANS read your articles and they are not kids, so they will flag your website if you write shit. However, this happens in spam queries/keywords (such as payday loans) and other super-tough competitive niches. Chances are, except the big players, you are not in one of them.
Eliminating the first option, we come to the 2nd one. An ALGORITHM, and a pretty good one (but with huge flaws as every complex algorithm is), decides where to rank your site. I am pretty sure you have all heard that Google is acquiring quantum computers, is getting better at determining article quality (algorithmically), is employing new AI systems bla bla... Maybe... Or maybe not.. The fact that in some niches you can still rank with spun content and sometimes pure shit/garbage one means they haven't yet.
So better get this through your mind.
However, that does not mean you can write entirely shit and expect to rank. After the LSI Update, Google can detect if your article is "relevant" enough by cross-checking its huge databases with your article's certain keywords. This means that if you want to rank for "dog training" and your article includes keywords such as "puppy training", "dog obedience", etc.. your percentages of ranking higher will increase. If you don't include them, they go down, because simply your article isn't "relevant" enough.
But this does not mean that, if you have a spun sentence that doesn't make much sense but you still include the necessary keywords, Google can detect that. Don't be stupid, you need logic for that and computers have their own logic, not ours.
And yes, bounce rate is a factor that determines where you rank or not. The whole reason we write engaging content on the first page is for visitors, because shit content = low conversions = no money. Not for Google. But write awesome content and skip the rules that the algorithm is made from and only your grandma will read that content, because it won't get ranked lol..
Clearing these things out, @OP: Yes, keyword density matters a lot, especially total page keyword density (not just the article). Please refer to phpbuilt thread, he explains it too much in detail and better than I would.