Some parents complain about anything at all. When I was a Youth Leader for my church, I received a phone call from the Associate Pastor asking about my Myspace page and expressing concern if there was anything inappropriate on it. Turns out a parent had gone on to my page and a liquor ad popped up (that Myspace put on in their ad banner, not me). So the parent called the Pastor expressing great concern that I was “promoting” alcohol to the teens in the Youth Group. When of course I wouldn’t do anything at all like that, nor could I choose which ads were placed on the site. So yes, I got the blame for this supposed “pushing of alcohol”. It happens. And yes, parents will call on it.
I think some have too much time on their hands. I'm not talking about reasonable complaints but the ones like you stated.