We made ( or I at least) an assumption you would know we meant a 2x4 with the 4 inch (3.5 inch) side up for the roost....not the 1.5 inch side up..
I agree your stick looks wide enough where the chicken is. As long as they can cover their cute little toe nails. The first picture and way you described it, it looked too narrow to me.
It is good to take everything you hear about chicken raising here and elsewhere with a pinch of salt. While I like to get others input, as it helps me decide, I never consider anything as gospel. There are as many ways to raise chickens as there are bellybuttons in the world.