Issuing a DMCA takedown that is both false and meant in bad faith is an act of perjury. In theory the copyright holder could get jail time.
A interesting case is the video of a toddler dancing on youtube, 29s long, to a song. The Ninth Circuit held that copyright owners must consider fair use before issuing take-down notices. The case got settled afterwards.
This difference between DMCA takedown and ID claim is often discussed by youtube creators as both a boon and a curse. The good thing is that id claim does not impact any future standing with google or legal punishment beyond the loss of revenue from the video that get claimed. The bad side is that they get abused.