What I thought - First the doctor tried to just divert the investigation by trying to frame the Minister by proving Ajit's father as the potential blackmailer and the deal gone wrong. When that didn't work, and the dying minister uttered "Yang Guang" or rather "Young Gun" as was deciphered wrongly by BB in front of Anguri Devi, as a defensive measure Doctor took all the blame upon himself with the freedom fighting angle so that BB doesn't even investigate any further.
Now going by the point you made
hereas if everyone thinks tht Yang=Guang is the killer then it would help the doctor because no one knows who Yang-Guang is and by doing that he could have kept his double identity and could have been with BB all the time and would know his plans in advance.
If somehow it was proven that Yang Guang was the killer, then it would not have been a big deal for BB/police to know the secret plan of Japanese invading the Kolkata which was the primary motive which Doctor/Yang Guang had to keep as a secret. Now since the Doctor confessed of killing, and if his plans had been successful then he would not have to stay underground anymore, as was said in the movie, the government after Japanese invasion would have been a puppet at the hands of Japanese Army and Yang Guang.
That's my take on the movie. Hope I could make some sense :)
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