Independence is important because it supports objectivity, which is the foundation of credible assurance.
Option D captures the key idea: independence (organizational and personal) reduces bias and conflicts of interest, enhancing the impartiality and credibility of conclusions. In practice, this means assurance providers (e.g., internal audit) should be positioned so they are not auditing their own work, are not responsible for operating the controls they evaluate, and have sufficient freedom to report issues without undue influence. Independence does not mean acting without governance oversight (A is wrong); rather, assurance results are typically reported to the governing authority or audit committee to strengthen oversight.
Financial independence (B) can be one aspect of avoiding conflicts (more relevant to external providers), but it's not the full rationale and does not alone ensure objectivity. And independence cannot guarantee no influence from external factors (C); it is a control to reduce influence and improve trust in the assurance process.