My dobie will only toilet at home ( outside of course) - she will not go in public.
Our Rottie will toilet when out for a walk, but will find the most secluded or inaccessible place to go.
Both look extremely shifty when they do go.
However, I was told that the reason for this 'look ' was becuase the 'wolf' part of their brain reminds them that they are vulnerable to attack from predators when doing number twos and as such they are at their most cautious and wary when toileting - we interpret their look as embarrassment, wheras in reality it is a look of caution and nervousness.
Thats what I was told anyway.