According to IIA guidance, the practice by the chief audit executive (CAE) that best enhances the organizational independence of the internal audit activity is meeting privately with the board at least annually.
This practice ensures that the internal audit activity can operate independently of management and directly report and discuss significant matters with the board, which is critical for maintaining its independence and objectivity.
The Institute of Internal Auditors (IIA) - International Standards for the Professional Practice of Internal Auditing.

According to the IIA Standards, the chief audit executive (CAE) must ensure that internal audit activities are performed with competence and due professional care. If the internal audit team lacks the necessary knowledge or skills to perform all or part of the work, the CAE must obtain competent advice and assistance.
Thus, the CAE's best response to defend the expenditure for an external fraud expert is to refer to the Standards, explaining that the internal audit activity must obtain competent assistance if needed to ensure the investigation is conducted effectively and professionally.
IIA Standard 1210: Proficiency

The IIA Standards state that conformance with standards related to independence and objectivity is not dependent upon the size of the internal audit activity. All internal audit functions, regardless of their size, must adhere to the principles of independence and objectivity to ensure that their work is unbiased and free from undue influence. This is fundamental to the credibility and reliability of the internal audit activity's work and findings. While small internal audit activities may face unique challenges, such as resource limitations, these challenges do not exempt them from maintaining these core principles.
The IIA's International Standards for the Professional Practice of Internal Auditing (Standards) - Standard
1100 on Independence and Objectivity.

The chief audit executive (CAE) is responsible for ensuring the professional development of the internal audit staff. This responsibility includes providing opportunities for ongoing training and development to maintain and enhance their competencies. References:
* IIA Standard 1230: Continuing Professional Development.
* IIA Practice Guide: Continuing Professional Development for Internal Auditors.

This action by the organization's board would potentially impair the internal audit activity's independence, because it would create a reporting threat that could undermine the CAE's ability to communicate the results of internal audit engagements objectively and directly to the board or the audit committee2. The CAE should have unrestricted access to the board or the audit committee, and should not be subject to any undue influence or interference from senior management in reporting the internal audit findings, opinions, and recommendations3.
References:
1: Standard 1110 - Organizational Independence - The Institute of Internal Auditors or The IIA
2:Independence and Objectivity - The Institute of Internal Auditors or The IIA
3: Position paper: Independence and objectivity | Delivering internal audit | Resources | IIA An internal auditor is assigned to an assurance engagement.