Our Siamese would also drink out of the toilet. And, whenever we entered her room and she was on her litter box, she would meow irately at us, as if she we were as embarassed as anyone else would be at someone walking in on them while on the loo.
My Lab is also very modest . . . to the point that she will back under a bush to do her business and look away if you are looking at her. It actually is nice, because you don't step in "surprises" walking across the lawn. On the other hand, sometimes her byproducts are hard to find when patrolling with the scoop . . .