Yes, but due to comma weaselling, the perjury but only refers to whether they are allowed to speak on behalf of the copyright holder they claim to represent, NOT on whether the material infringes that holders rights.
So they could file a takedown notice claiming that the constitution of the USA infringes NASCAR's rights, as long as they are allowed to speak on behalf of NASCAR.
They could not file a takedown notice claiming an actual NASCAR race recording infringes NASCAR rights, if they did not have the right to speak on behalf of NASCAR, even though that recording actually does infrige.
But IANAL, so I might be wrong.