Okay, let's break this down. You're right to question the inspector's ruling. Here's a detailed explanation of why the LFMC likely should provide sufficient bonding in your scenario, and potential reasons why the inspector might have raised the issue

Understanding the Core Concepts
Bonding

Bonding is the intentional connection of metallic parts (enclosures, raceways, etc.) to create a low-impedance path back to the source of power. This path facilitates the operation of overcurrent protective devices (OCPDs) like breakers or fuses during a fault. It also helps minimize voltage potential differences between metallic parts, reducing the risk of electric shock.

Equipment Grounding Conductor (EGC)

The EGC is the conductor (or conductive path) that connects normally non-current-carrying metal parts of equipment to the system grounding electrode conductor, the grounding electrode, or both. Its primary purpose is to provide a low-impedance fault current path.

LFMC (Liquidtight Flexible Metal Conduit)

LFMC is recognized as an EGC under specific conditions (NEC 250.118).

Why LFMC Should Be Sufficient Bonding

According to the NEC 250.118(5)(a) LFMC must have fittings that are listed for grounding and if the circuit conductors contained in the LFMC are protected by overcurrent devices rated at 20 amps or less for trade sizes 3/8" through 1 1/4" and overcurrent devices rated at 60 amps or less for trade sizes 1 1/2" through 4". NEC 250.92(B) requires metal raceways to be bonded The 3/4" LFMC with listed fittings should be considered to be sufficient for bonding a junction box.Reasons the Inspector May Have Raised the Issue

Even though LFMC can be an EGC, here are some possible reasons the inspector might have cited the installation:1. Fittings Not Listed for Grounding

This is the most likely reason. The fittings used to connect the LFMC to the junction box must be listed for grounding. "Listed" means a recognized testing laboratory (like UL) has tested and certified the fittings for this specific purpose. Standard LFMC connectors may not be listed for grounding. Look for markings on the fittings like "GRND" or specific UL listing information indicating grounding capability. The lack of proper fittings would render the LFMC not an acceptable EGC.2.

Loose Locknuts

Even if the fitting is listed for grounding, loose locknuts can compromise the electrical connection. Locknuts should be tightened properly to ensure good electrical contact between the fitting, the box, and the LFMC. It is best practice to use a locknut on both sides of the box when using metallic raceways.3.

Fault Current Capacity

While unlikely with the sizes you're describing, in very high fault current scenarios, the inspector might be concerned about the ability of the LFMC to handle the fault current without damage. This is usually only a concern in very large service entrances or industrial applications with exceptionally high available fault current. If the available fault current is above the listed short circuit current rating of the fitting/LFMC system.4.

Shielding vs. Bonding/Grounding Confusion

You mentioned the inspector said the shield of the conductors could be used for bonding. This is an entirely separate issue and could indicate a misunderstanding. Cable shields (like those found on shielded cables) are often bonded, but their primary purpose is to reduce electromagnetic interference (EMI) and radio frequency interference (RFI), not to serve as an EGC for fault current. While a cable shield can contribute to grounding, it is usually not the sole means of providing a fault current path and should not be used for bonding alone.5.

Local Amendments/Interpretations

It's possible the local jurisdiction has amendments to the NEC or a specific interpretation that is stricter than the national code regarding LFMC as an EGC. Always check local regulations.

Recommendations1. Inspect the Fittings

Carefully examine the LFMC fittings. Are they clearly marked as "GRND" or listed for grounding? This is the critical first step. If they aren't, that's the problem.2.

Ensure Tight Connections

Make sure the locknuts are properly tightened. Use two locknuts one on either side of the enclosure.3.

Consult the Inspector

The best approach is always to have a respectful discussion with the inspector. Ask for clarification on exactly why they cited the installation. Refer to NEC 250.118 and explain that you believe the LFMC, with proper fittings, meets the requirements for an EGC.
4.

Provide Documentation

If the fittings are* listed for grounding, have the documentation (UL listing sheets or manufacturer's specifications) available to show the inspector.5.

Add a Supplemental Grounding Conductor (if necessary): If the inspector is still not satisfied, even with proper fittings, the easiest solution might be to install a separate grounding conductor (green wire) inside the LFMC and bond it to the box. While it might be technically redundant, it will likely satisfy the inspector and avoid further delays.In summary, the key is to verify that the LFMC fittings are listed for grounding and properly installed. A respectful and well-informed conversation with the inspector is usually the best way to resolve the issue. Flag for review