That's correct Motori jaan, IATA mainly cares about NAV/COMM facilities and movement surfaces, and less for passenger facilities. IATA membership of Iran Air does require compliance with its rules, but they are not that complicated and membership, although much more desired than non membership, is not such distinction in pilot training as it includes many poorer countries too:
See all IATA Member Airlines Reputable airlines always far exceed this lowest common denominator. While Iranian aviators may be among the best, its policy makers are not!
As well, keep in mind that Foreign carriers flying into Iran has to do with satisfying their own safety and marketing schemes, and managing risks. It may be acceptable risk to do non-precision approaches to landing in areas where the weather is visual 95% of the time. Plus the great majority of foreign carriers and international flights in general go through Tehran which does have adequate NAV/COMM facilities, but other major cities in Iran like Urumieh, KhoramAbad, Hamedan, Kermanshah, maybe even Abadan and Ahvaz don't even have an ILS! In the U.S, every little airport has multiple ILS and there are VORs every 15-20 miles, not the same in the fatherland I'm afraid. Unfortunately hazarat are busy building nuclear "stuff"!