One who shits in a bin, wherever it may be, the street, a shop, even in a toilet. Although, usually not a bin in a toilet, what would be the point in that? However, a binshitter does not have a head brimming with brains. His head is more like brimming with shite. So shitting in a bin in a toilet is not as absurd as one may think.
(binshitter): "Man I need a shit and I need it right now! That bin on the lamp-post over there is a little high for me but I must get my ass up there to unload my goodies"