Has anybody asked any rental car company rep why there is such a discrepancy between the companies' website policies...and their actual on the ground policy in Iceland?
What discrepancy?
It's not the job of the guy at a rental car counter to ensure you know and comply with the local traffic laws - that's the driver's responsibility, not his. If a driver gets thrown in jail after an accident because it turns out they were not driving legally, the rental guy will be free and walking around without a care in the world. The driver, on the other hand, might be in serious trouble, as it's their responsibility to fulfill all the legal requirements to drive. The rental agency will get their car back, that's what they care about. What happens to the driver, not so much.
Now, some companies may have a POLICY to warn customers about legal requirements, and individual employees might take it upon themselves to do that as a courtesy (in reality, very few do), but nobody should rely on them for that, since they have zero responsibility for enforcing the traffic laws.
I've probably rented cars over 100 times all around the world on every continent except Antarctica. I don't recall ever being asked (or told) to show an IDP. Give them my reservation number, wave the credit card, show my passport, maybe show my Washington state drivers license, sign here, here and here, initial there, there, and there, here's the keys, off you go. In all cases, if an IDP was required (or even suggested), I definitely had one (including in plenty of places that use the Roman alphabet). But that is generally not part of the car rental ceremonies.
AFAICT, no place in the world legally requires you to show an IDP to RENT a car. Plenty of countries do legally require you to have an IDP (or other legally-valid translation of your otherwise valid license) to DRIVE a car (if you don't have a local license).
Personally, I have always been very glad I had the IDP with me whenever I've been behind the wheel in a foreign land, whether that was when a Spanish cop pulled me over for speeding on my first trip to Europe, or when a Japanese cop jumped out from behind some bushes and flagged me down after I had just passed a truck in a clearly-marked no-passing zone, or when I went past a parked police car in France and saw them pointing a radar gun at me.
It also occurs to me that if someone was driving through my home town, ran a stoplight (or god-forbid, hit a cyclist), and when the police showed up they handed over a drivers license from Algeria or Zimbabwe, things might not go well for that driver. To me, having the IDP ready just-in-case is a small convenience and a courtesy that I can provide for any automotive or legal authority figure whom I might encounter. The term "cheap insurance" also comes to mind, and the $25-$30 the IDP cost me seems like small potatoes, but maybe that's just me being paranoid. I know some folks seem quite antagonistic towards the IPD and view it as highway robbery. YMMV.