Is the inspector the AHJ?

AHJ (or AWJ) is the authority having jurisdiction (or authority with jurisdiction). That brings up two questions: What authority and what jurisdiction? The authority or jurisdiction to enforce a standard is not ever the same authority to adopt that standard. To adopt any standard, there are requirements such as voting or publishing. No single person could ever hold that authority over another person. While an inspector may have influence, their role as code enforcement is to enforce that standard, not create it. Enforcing any standard or law that has not been adopted removes qualified immunity.  The role of inspector is not adoption.

Interpretation

In many cases an inspector may interpret standards for electricians but their interpretation of a standard is not the standard, it's literally their own interpretation of it and not ever enforceable.

“...their interpretation of a standard is not the standard..."

Approval (or Approved means)

This is a contested matter that should really have more definition.  Does an inspector have the authority to"approve" or "reject" anything?  They enforce they do not create a standard. For instance wire has to be supported in an approved manner.  Who approves it?   More often than not that approval is given (or not given) by an inspector that doesn't have the authority to grant it (or deny it).  Inspectors are being thrown under the bus when they are given that authority.  An opinion can not ever be a standard.

Authority is given not taken