I have no idea what the bathrooms at this school are like, other than the article indicates that there are separate boys' and girls' bathrooms that are in general use by his class, and a few unisex* bathrooms do exist in another part of the school--presumably farther away--and the child in question will specifically go to use those whenever he needs to go.
In the two elementary schools I attended, as well as two others I have been inside as an adult, classrooms are connected in pairs (usually both the same grade) by a short hallway between them, which is not the main hallway of the school. Within this connecting hallway are two doors leading to bathrooms, one for the girls and one for the boys. I've also seen private places like preschools and daycares use this floorplan. Maybe that's just standard building procedure in Texas, I don't know. By the time you get to junior high, the bathrooms are higher-capacity and accessible from the main hallway, like in any public place.
*As for the definition of
unisex, well, it is what it is. The Latin roots may not make the most sense, but very little in English makes sense anyway...