I think you do not quite understand it correctly. When there is a "nie" involved, a direct object in the Accusative changes to a object in the Genitive. As it happens, though, being masculine animate, the Genitive of "kot" is the same as the Accusative: they are both "kota".
"Moi chłopcy widzą kota." but also "Moi chłopcy nie widzą kota."
If it were "cats" rather than "a cat", then that would be a different story :-) !