Playing "Devil's Advocate" here, but if the dog is on the homeowner's property (which it was), and not running loose in the streets or outside of the property boundaries, the homeowner has the RIGHT to use his property as he wishes as long as that use is within the law.  In this case, the homeowner had a RESTRAINED dog and was "using" his property within the law.  Just because you can't see the fence, doesn't mean it did not exist.  Most invisible fences also have "marking" flags for the boundary to let others know that it exists.  None of us can, however, make that assumption.  You begin treading on dangerous ground when you start "advocating" for rules/circumstances that dictate "specific uses" for front versus back yards as your statement clearly hints.