Are there known cases where people can write upside down?
Leonardo da Vinci wrote both upside down, and in a mirror image.  He did the latter partly to make it harder for others to read his journals and copy his ideas (he was doing his research in a time when it was forbidden by the church), but also to avoid smudging his writing.  He was also left-handed.

Here is someone who also writes upside down and backwards.  And here is a case of a mother asking if she should be concerned because her 2 1/2 year old daughter writes upside down.