My cat is named Max too...LOL! He goes outside and usually does his
business there, and he had just been outside, which makes me think
it's just spite somehow. He started doing it when I had put him into
the bathroom to allow my mother to east as he was all over her. He
left a large brown present on the rug, and now pees in the same spot.
I looked up urinary infection in cats and he doesn't lick himself
there at all. Another site suggested he wants to be like his owner and
use the bathroom like they do and sleep in a bed too. His box is clean
and private. He is crapping on it as well as peeing, so there has to
be something else going on that displeased the little sh.t!