Check out the link profile of the site whose links Google doesn't like
I don't see how this really has any bearing on natural links being identified as unnatural, and I surely don't see how many small businesses/webmasters can inspect the backlink profiles of not only their sites but also of everyone who links to them.
Those who run quality sites, and I'm not talking about the typical thin sites that are produced these days, will have a certain level of unnatural links. Providing depth, useful details, videos and detailed photographs has its drawbacks. Often link spammers will throw other links in their spam pages to make their spam appear real with authoritative references. These types of links, which are unnatural, do trigger penalties that demote innocent sites that are linked to in spam pages merely because they have taken the time to innocently produce quality content.
The bottom line is that Google has webmasters running in circles chasing their tails like dogs. Sooner or later these dogs will grow tired and pause to think about what they are doing, why they are doing it, if they can ever catch their tails and what benefit it produces if they do.