You are simply wrong. Google is very clear that link building by promoting your business in a normal manner on the web is not the same as back-linking to influence the SERPs. Why do you think relevancy and quality play so important a part in the algo?
First off, SEO wise your on-page must be correct for them to even understand what the web-page is about. Without that people will come to your site looking for something not there.
The idea that you are not supposed to link on the internet is absurd, it can't exist without links.
Linking your business with Linked-in, Facebook, Twitter, your suppliers, your business associates, players in your niche, discussions about your niche, and so on will not hurt you because it is a normal thing for a real business to do. Commenting on related publications is business promoting, not spam.
Real business sites don't have link wheels wrapped around them, or build thousands of links consistently. They don't link to crap places and spun articles. If they publish, what they publish is top notch, their business reputation is on the line.
You will never get punished for behaving like a business and participating in your niche.