Your "friendly" DOT officer is full of it. There are one set of rules (nation wide) not all of are good, but it's what we have.
Depending on what you're hauling and which type of securement system you use....... but let's say you're hauling bundled pipe, lumber, etc. You should have tightening (binders, ratchets, etc) on both sides. Example: Ever seen a load as described above secured by straps and all ratchets are on the same side? When you tighten down, you're pulling all in the same direction, that's when you get a "blow-out" load. They should be alternating from one side to the other.
If you look at flats, steps, etc with mounted sliding ratchets, many will place them all on the street (driver) side. None of my rigs are setup this way. And further more, if you read (carefully read) the current load securement ruleing, you are to "alternate" the tightening devises from side to side.
If you are using chains on an excavator for example; You must have independent securement in all horizontal directions, how are you going to chain the the street side tracks with no binder? Do you really think you'll pull the curb side tight enough to tighten the street side?
Sounds like your "officer" went to the 2-hour ticket writing class. Good luck