Trying to word my thoughts about this simple experience -
Attention to detail - They could've put a "twitter is busy" message and would've been fine, but they want to take care of every part of the user interaction. Guarding the image they have in the users mind.
Little bit of cuteness goes a long way - The unpleasantness of my experience was greatly reduced.
Impression - Seems like the group of people who created this would be a great "bunch" to work with 8-)
If you guys have come across a great "Service unavailable" picture, please let me know, would be fun to see them !
Keeps the creative juice flowing.