It seems that the situation with the HOA Management company and the homeowners has become quite contentious. From the facts presented, I agree with your assessment that the Board members or the HOA likely would not be liable to the employee or the management company.
No Liability for Individual Behavior: As you correctly recognized, the HOA is not a police force and is not responsible for individual homeowner behavior. Since the aggressive homeowners were not employees or agents of the HOA and were not acting on behalf of the association, it does not appear that the HOA would be liable.
Consideration for New Management Company: Given the current tensions, it may indeed be time to consider finding a new management company. To replace the management company, you should review your governing documents and determine who has the authority to change companies. It is likely well within the board's powers.
Consult with Legal Counsel if Needed: While it seems that the situation is clear from your perspective, if the management company continues to press the issue, you may still want to consult with legal counsel to ensure that all bases are covered. Feel free to reach out to us if you would like to discuss your concerns with an attorney.
Document and Communicate: Continue to document all interactions and decisions related to this matter. Clear communication with the management company about your stance and the reasons behind it may help to resolve the issue.
Implement Identification Requirement: Moving forward with the requirement for visible identification for all employees conducting site visits is a sensible step to prevent future misunderstandings.
Your approach seems well-reasoned and aligned with the responsibilities and rights of the HOA. If the relationship with the current management company has indeed soured, following the proper procedures to find a new one that aligns better with the HOA's values and expectations would be a prudent course of action.