It specifically says "I swear, under penalty of perjury, that I am the copyright owner or am authorized to act on behalf of the owner of an exclusive right that is allegedly infringed."
See that's the thing: I read that as "I'm saying that Product X is being infringed and I swear that I am authorised to act on behalf of the owner of Product X".
It is not saying that "I swear, under penalty of perjury, that that the product I claim is being infringed actually is being infringed".
I don't unfortunately. The discussion I read was so long ago that it was probably on Slashdot :) Having said that, I found a few sites with 'DMCA policies' (eg. http://www.azlyrics.com/copyright.html ). Looking at how they discuss perjury, as well as just reading that line that you quoted nothing mentions that you are claiming the infringement under perjury, just that you are allowed to represent the product that is allegedly being infringed.
So, if you're not the copyright owner...