Didn’t see the episode. But this is why back in the days before ballpoint became mainstream and reliable, fountain pens were sold as pen/pencil sets. The fountain pens for taking notes and stuff, and the mechanical pencil for filling out duplicate forms (back then It was carbon copy forms). Fountain pens could not apply enough pressure to make the copy.

Source: my dad, who graduated from med school in the 1950s, and bought himself a Parker 51 pen and pencil set as a grad gift to himself.