I'm guessing it's the economics of it he's objecting to. It's probably going to take you longer to bury it and thus cost more than it is to un-reel it and simply cable tie it to a railing.
I'd be looking for technical reasons that you could use against it... is it a much longer run? If so, run the numbers for voltage drop and predicted Zs at the end of the run. You may need to use a bigger cable and obviously the cost increase is proportionate to the length, that could be enough to tip it if it's just the economies he's thinking about.
You could also raise the issue of mechanical damage (and any other external influences that may be relevant to the 'yard'). You mention trucks. SWA is fairly tough against a spade, but I'm fairly confident it won't do so well against a 'truck'. If there is a lot of vehicular traffic, accidents do happen. And if he comes back with something like well they'll hit the railing first, you can suggest that because it's attached it's entirely possible a larger section of cable will be damaged in a single incident requiring the expense of new cable and resin joints, although I suspect he might suggest choc-blocks and PVC tape is sufficient
The potential for damage comes into play if what is going on in the office is critical to the business? If it's a sales function for example, no sales = no money (business won't like), no power due to damage of cable = no sales (most businesses rely heavily on PCs, no power = no PCs). The criticality of infrastructure and business function is sometimes a useful weapon. Half a days lost productivity in the cabin could cost more than the time taken to bury the thing in the first place.
I'm with Pete, I'm assuming he means this... do the job properly and bury it. It's safe and sound then.
I've never understood why people fix it to their fences either. And if you think his decision might come back and bite you in the a$$ down the line, I'd be sending him an email highlighting your concerns