Well, I saw according to the Muppet Wiki that on DVD, the "Public Transporation" segment of "Elmo's World" had the Peanuts theme replaced during Dorothy's fantasy of Elmo flying a plane, AND the "Chattanooga Choo-Choo" theme replaced during the fantasy of Elmo driving the train.
Unfortunately, they cut the film with Mark and his mother riding a commuter train to visit his grandfather. I imagine this was also due to music rights, as you can hear the "Chattanooga Choo-Choo" song during it, along with an instrumental of "Down By the Station." I uploaded that film segment right here, as it's probably one of the first times a diesel train was depicted on the show (footage of the Long Island Railroad, to be exact.)
Too bad they couldn't just take this segment without music (if it exists) and simply re-score it.