This is incorrect - it's an issue between the copyright owner and copyright infringer, with the content host only acting as a relay.
Under Section 512 the only responsibility of the service provider is to remove the content, relay the notice to the actual copyright infringer, and allow them to file a counter-notice.
From there if the counter-notice isn't accepted by the copyright owner, they would have to file a lawsuit with the copyright infringer.
But if the platform ignores the DMCA takedown, the alleged infringer will never know, and so cannot sue.
I think the original question is if the platform can sue the person sending the DMCA takedown, for some kind of harassment. Because the platform itself will also investigate before taking content down.
As long as the platform follows a proper DMCA takedown, they cannot be sued for infringement. If, however, the platform ignores the DMCA takedown, they lose the protection they'd otherwise keep under the law and can themselves be held liable for the infringing copyright.
The problem with the DMCA is that the platform has to immediately take down the content or they lose the protective aspect of the DMCA- I think (though not a lawyer) that more or less any analysis immediately strips protection.
Essentially the belief is that DMCA would never be abused for any reason so you need to penalize the platform but not the submitter.
Under Section 512 the only responsibility of the service provider is to remove the content, relay the notice to the actual copyright infringer, and allow them to file a counter-notice.
From there if the counter-notice isn't accepted by the copyright owner, they would have to file a lawsuit with the copyright infringer.