Section 7434 is "Civil damages for fraudulent filing of information returns." It's not clear that there is any fraud, or that the 1099 that the client issued is incorrect. The client made payments to an individual contractor who gave them her Social Security number, and they correctly reported those payments on a 1099 issued to the individual who was paid. The client did not make the payments to an S corporation. Most likely the specifics of the contracting arrangement were not clearly spelled out in advance. We don't have all the details. There may not be a written contract. The two parties had different understandings of the arrangement. The contractor may have given the client a W-9 that did not properly reflect the contractor's intentions concerning how payments were to be made.
