If your site was precisely the same age, with the same kinds of content and about the same organization and number of pages, then yes, it would be a horse race. But of course that is never the case.
The thinking behind the tactic you mention is simply that if those sites are linking to your competitors, and you have an equally good or better site, then those sites may also be interested in linking to you. It's more an SEO 101 starting point; a basic base to cover.
The trick then is to create more/better content, and market your site more effectively, and listen to your user base. Also ask yourself two questions:
1) What are your competitors doing that you could do better?
2) What are your competitors not doing, that should be done?
