I always get frustrated with those signs...if they mean no trucks because they don't want semis using the road as a shortcut, then I would say it doesn't apply. Sounds like that is the case with your neighborhood road.
But how do you know "no trucks" isn't for a reason? Like road too narrow, turn too sharp, bridge too low? It's the operator's responsibility to know that his vehicle can safely travel the route he chooses, so without knowing the reason for a "no trucks" sign I generally avoid routes posted as such.