I don't know whether it's well-known(?), but the parody story of the dog quoted in the article seems based on a better parable:
Aspiring young monk is given the honor of joining a prestigious monastery. While traveling there, he is stopped on the road by a ragged-looking person who needs help. Monk says get out of my way, I'm important, and in a hurry to meet the head of the fancy monastery! When the monk gets to the monastery, well, you can guess that the head of the monastery was that ragged person, and that there's some remedial lesson in monk-ing.
Aspiring young monk is given the honor of joining a prestigious monastery. While traveling there, he is stopped on the road by a ragged-looking person who needs help. Monk says get out of my way, I'm important, and in a hurry to meet the head of the fancy monastery! When the monk gets to the monastery, well, you can guess that the head of the monastery was that ragged person, and that there's some remedial lesson in monk-ing.