After watching it in detail, there is definitely no mention of smoking anywhere in Episode 37.
Interesting. Was there any evidence that it was re-shot after its original airing? I find it hard to beleive that the University of Pittsburgh files would be that wrong. So I'm guessing that they probably edited it after its original airing to remove the smoking. Either that, or it confused it with another episode. I copied the description below. Does this sound anything at all like the episoide that you saw?
Summary:
Mr. Rogers paints with water colors. He talks about how he is sometimes angered by Mr. McFeely's smoking. Mr. Rogers finds two pieces of chalk on his porch. Peggy Lipschutz uses the chalk for drawing while Vivian Richman sings.
In the NOM, Coach Saunders exercises with X and Daniel.
Contents:
Songs: Won't you be my neighbor? Let's go right away, Tomorrow.
Credits:
Producer, Fred Rogers ; director, David Fu-Ying Chen ; musical director, John Costa ; consultants, Margaret B. McFarland and Albert V. Corrado.
Performers:
Neighbors: David Newell (Mr. McFeely), Willie Saunders, Peggy Lipschutz, Vivian Richman, Charles Cubolic, Sol Davidson. -- Puppets: Daniel Striped Tiger, X the Owl.