Final answer:
The responsibility of ensuring that the auditor is independent in appearance falls on the auditor, in line with Sarbanes-Oxley and PCAOB rules. All parties, including the audit client, PCAOB, and SEC, play a role in supporting auditor independence.
Step-by-step explanation:
Under the Sarbanes-Oxley Act and PCAOB rules, ensuring that the auditor is independent in appearance is primarily the responsibility of the auditor themselves. However, the audit client, the PCAOB, and the SEC are all involved in creating the environment and regulations that support auditor independence. It is essential for auditors to maintain both independence in fact and in appearance to uphold the integrity of the financial reporting process.