Very unlikely it happened at that time. Maybe several years later; first Jagjit Arora retired, then Jake was transferred out (he came back as GOC-in-C just before retiring).
Something funny about this account. All the camps were run by the Home Ministry, under an officer whom we all knew. The only records in Fort William could have been details of training given, and of the individual officers detailed for liaison, such as Shabeg Singh, who got into a lot of hot water, crossing over with his trainees on more than one occasion. Until November, it seems that the orders were very clear: scandal was to be avoided at all costs, although everyone and his uncle knew that the provisional Bangladesh government was esconced in a building on Theatre Road.
Anyway, it is a fact, it was widely reported at the time, that the military records were found missing. My guess is that it happened during the tenure of N. C. Rawlley, who came in between Arora and Jake. I would like to believe so, for various reasons. Jake was given to exaggeration, but I don't think he would tell an outright lie.
PS: Interesting you should mention P. N. Haksar. He fell out of favour very soon after Bangladesh, Sanjay Gandhi disliked him intensely. D. P. Dhar sounds likelier; he had a finger in the Bangladesh pie, and oversaw a cabinet minister going to meet the Bangladeshi provisional government, to reassure them on several counts. He also lasted quite long, and outlived Sanjay Gandhi.