My knowledge of wildlife in general, and Warner Brothers cartoons in specific, cause me to have no trouble believing that coyotes would become relatively more carefree in the absence of a rottweiler.
Hopefully someone with more coyote experience can comment. We used to have a lot more coyotes around than we seem to lately. My wife speculates that the bobcat that now frequents the area cuts down on the coyote presence. I can report that two decades worth of our occasionally free roving beagles and labs (our current black lab is outside right now making the farm safe from heffalumps and/or deer) have never had trouble from the 'yotes or bobcats, only road traffic.