Google has changed up its wording from “There’s almost nothing a competitor can do to harm your ranking or have your site removed from our index.” to this lovely bit of scary wording;
Google works hard to prevent other webmasters from being able to harm your ranking or have your site removed from our index. If you’re concerned about another site linking to yours, we suggest contacting the webmaster of the site in question. Google aggregates and organizes information published on the web; we don’t control the content of these pages.
It’s pretty safe to say competitors can harm your site with links if done right, especially if you can do it yourself….they’re not going to be able to tell. There has yet to be any big and legit sites having a problem with links as it has mostly heen lousy affiliate sites. Most of the people complaining in the webmaster forums and Google’s help section have had not so good sites.
I’m not sure what else to say on this topic other than just focus on building up a real brand with more value to it that a set of links pointing to your site. What does your user want (apps, user engagement, deals, give aways, great content etc)? All of our clients that focused on these aspects have not been touched at all by any of the algorithm changes over the years, so it is possible to do good by Google.
Read it yourself: http://support.google.com/webmasters/bin/answer.py?hl=en&answer=34449