Okay, this is a common point of confusion, so let's break it down according to the NEC (National Electrical Code). Your co-worker is partially correct, but misleading.

The Short Answer: Yes, you DO need to bond metal pull boxes.The Detailed Explanation

Here's why you must bond the pull box, and the relevant NEC sections:

NEC 250.4(A)(5) Bonding of Electrical Equipment

This is a cornerstone requirement. It states that metal parts of electrical equipment that are likely to become energized shall be connected together and to the supply source in a manner that establishes an effective ground-fault current path. A pull box, being a metal enclosure containing energized conductors, falls under this requirement.

NEC 250.92 (Bonding Jumpers)

If you are piping to the pull box with RMC/LFMC, you are relying on the conduit fittings for grounding. When the conduits enter and exit the pull box through concentric or eccentric knockouts a proper bonding jumper is required. Since you installed pull boxes in lieu of conduit bends, then the bonding of the enclosure is a proper installation.

Effective Ground-Fault Current Path

The main purpose of bonding is to create a low-impedance path for fault current to return to the source. This low impedance ensures that a ground fault will cause the overcurrent protective device (circuit breaker or fuse) to trip quickly, clearing the fault and minimizing the risk of electric shock or fire. A poorly bonded (or unbonded) pull box can become energized during a fault, posing a shock hazard.

Not a Splice Box, but Still an Enclosure

The fact that it's just a pull box (no splices) doesn't exempt it from bonding requirements. Any metal enclosure containing energized conductors needs to be bonded.

How to Bond the Pull Box



Equipment Grounding Conductor (EGC)

This is your primary method. The EGC (the green wire) that you're pulling along with the 2/0 conductors MUST be connected to the pull box. Use a grounding lug or other listed connector suitable for connecting the EGC to the metal enclosure. The size of the EGC is based on the size of your OCPD as per 250.122

Why your coworker might think otherwise

Your coworker might be thinking about a scenario where the conduit system itself is considered the equipment grounding conductor. However, even in that case, you have to ensure electrical continuity of the conduit system through the pull box. Since you stated that you are using LFMC in the system then you will need the EGC regardless.

Important Considerations



UL Listing

Ensure all connectors and lugs used for grounding are UL-listed and suitable for the conductor size and the application.

Torque

Properly torque all connections to the manufacturer's specifications. Loose connections can increase impedance and compromise the effectiveness of the grounding system.

Inspection

Your electrical inspector will be looking for proper bonding of enclosures like pull boxes.

In Conclusion:

Always bond metal pull boxes that contain energized conductors, even if they don't contain splices. It's a fundamental safety requirement in the NEC. Your electrician instincts are correct – connect that equipment grounding conductor to the pull box! If your coworker disagrees, kindly point them to NEC 250.4(A)(5) and 250.
92. When in doubt, always err on the side of safety and code compliance. Flag for review