Actually, the DMCA doesn't say that. Many people have been misled because some of the popular "copy and paste" form letters for sending the notices include a different statement than is actually required.
Here's the actual text of the DMCA (HR 2281) [1]:
> A statement that the information in the notification is accurate, and under penalty of perjury, that
the complaining party is authorized to act on behalf of
the owner of an exclusive right that is allegedly infringed
You are only swearing, under penalty of perjury, that you're the owner of the copyright or authorized to act on behalf of an owner of the copyright. You are not swearing that you believe an infringement has occurred, or to anything else in your notice.
Thus even if you know the other party is not infringing your copyright, you are not committing perjury by attesting that they are infringing to a service provider. I don't know if there are other consequences of false takedown notices, but the swear under penalty of perjury doesn't actually exist.
1: http://www.copyright.gov/legislation/hr2281.pdf