There are leash-free areas, which is where I take mine, and some of those areas include bike trails.  I also take my 3-year-old granddaughter.  It's a great way for her and the dog to get fresh air and run around.  We often run across people biking.  There are signs in the area that indicate this is a leash-free dog park.  It's been my experience that the bikers see these signs and ride accordingly.

I believe the dog incident you're speaking of occurred on a street next to someone's yard when a new neighbor was moving into his home.