I get several referrals like that too and when I follow the referral, I cannot find a link to my site anywhere. They aren't competitors. One in particular keeps showing up as a referral from an on-topic site to mine but there isn't a link anywhere. Any other explanations?
Multiple browser windows being open? There's a glitch sometimes with multiple windows being open. Your competitor might have two or three browser windows open (one for his site) checking what else? The competition, and it might show up in your logs as a referral.
Very strange. I have also had as many as 18 mystery referals from a page that had no links to mine. And several other cases with four or five. I have also been puzzled by this phenomena for about two months. Digital ghost's explanation sounds reasonable but not for 18 referals from one page. Hmmmm.