I don't think folks are suggesting that people be lax when around big dogs, but maybe that small dogs have a nature more in line with those worries. I've been around dogs a lot and a very good rule of thumbf for me is that the smaller dogs are the more aggressive, jumpy ones. This isn't steadfast truth, it's just way more common in my experience.
Our 250 # english mastiff is outstanding with kids. If a baby is crying, he'll go to the crib and circle it until someone comes. He'll let the little ones climb and wrestle all over him without returning even the slightest force or agitation. If I'm playing around with him though, he'll return and bit more and 'rough house'.
I've only rarely met small dogs with a good temperment, that didn't bristle up and bark at everything that moved. That infernal yapping would be enough to make me take a return trip to the pound.