The USAF itself flew 648 sorties, of which 599 were SAR missions, rescuing 4322 people. The national guard, army, navy, marine corps and coast guard together rescued 15,000 people by helicopter. In other words, the entire US war machine was involved. The IAF alone rescued 20,000 by helicopters. The army aviation wing also evacuated a smaller number by helicopters.
http://www.afhra.af.mil/shared/media/document/AFD-070912-046.pdf
Also, the terms "evacuation" and "rescue" should not be confused. In case of Katrina, most of the airlift was to evacuate people from shelters like the super dome. In Uttarakhand, the airlift was mostly to rescue people from mountain tops that had never seen roads or electricity or telephone poles, and jungles and ravines. Isolated groups of small number of people had to be searched for and evacuated by helicopters as well as special forces. That is very different from flying thousands of people huddled together in shelters to other cities.
The total number of people termed as "rescued" by the helicopters of all the US forces is 15,000. Of which 4322 were rescued by the USAF. So I suppose the IAF can still claim a record. In any case, for issues like this, statistics and records are secondary. What is important is that the IAF successfully averted a huge impending tragedy, when an unexpected cloud burst happened at the wrong place at the wrong time (during the pilgrimage season).
So record or no record, the job done by the IAF was commendable.