Just had another idea actually: what if the old man is lying? He might be a friend of B-1 and B-1 is trying to make Eiji confused. Something like this:
B-1 knows that Eiji will go to the doctor to check on the multiple personality disorder -> B-1 goes first instead -> there, he meets the old man and convinces him to help him -> they establish a codeword (the whole "give me a cigarette" shenanigan) -> B-1 tells the old man to lie and say that Kyouka was there with him if Eiji/B-1 does not give him a cigarette
That could be interesting though, and it is not too confusing either, it could work from a storytelling perspective. I just have no clue over the motive yet xD