Sorry but no! The AHJ can call anything they want service equipment but if is on the utility side of the demarcation point only the name in the National Electrical Safety Code (NESC) has any legal effect on what it is for code enforcement purposes. Do keep in mind that the enforcement of the NESC is the exclusive province of the State's utility regulating agency. I have never encountered any electric utility that will allow me to touch anything that they install or maintain.
Side observation: What I have seen in many places is a utility owned pole at the property line or in an easement that supports the utility end of what is technically a service drop; in spite of it looking exactly the same as the rest of the POCO lateral: which extends to, what many rural utilities call, a yard pole. Yard poles are customer owned even though they MAY look like all of the rest of the poles on that line. I have also seen utility owned rod operated pole-top switches on the last POCO owned pole. At the bottom of the Yard Pole there was often a Current Transformer (CT) type meter. From the top of the yard pole the individual drops extended to service equipment which was mounted on or in each building. The other arrangement which is becoming more common is for an underground Service Lateral from the last utility owned pole to come up to a Meter Mains assembly or to metered conductors in a trough supplying multiple disconnects. The feeders from those 1 to 6; but usually one more than there are buildings; then go underground, or even overhead via a Yard Pole, to the Building Disconnecting Means at the individual structures. The additional Service Disconnecting Means, over the number of structures served by the other feeders, is the one that supplies the water pump that is also used for "First Aid Firefighting."
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Tom Horne