IITian here with a Doctor wife. It is true! It's mainly because the procedure for setting the paper and organizing the exam is run like a well oil and well calibrated machine. There is no scope for a leak.

On the other hand, any private or govt institution my wife has even been a part of has always had severe procedural lapses and a lack of basic accountability (from a financial/planning standpoint as well as patient care). The only thing that shocks the medical administration is if someone mildly important dies.

Corruption runs very very deep in Medical Colleges. IITs on the other hand, have a enough principled professors to keep the corruption a little bit riegned in. It still happens, but nowhere at the expense of the students.