I imagine the research about non-verbal communication in humans would be instructive here. A relatively small minority of our in-person communication actually comes from the spoken words. The rest comes from body language, tone, inflection, and so on.
I wonder how much of that a dog or similar animal picks up on regularly? Could it be that they actually pick up on the majority of our communicated meaning?
What's more, I wonder if we are we actually poorer communicators than animals, because they understand our messages better than we understand theirs?