I haven't heard or read anything about this, but she was really concerned. If you are concerned that pet rats would transmit disease to your children, then no, you really have nothing to worry about. That is no more likely than with having a dog or cat as a pet. Of course, it is possible, but not likely, in any case. Your friend must be buying into the prejudices that most people have concerning rats.
Zoonoses are diseases that can infect humans and be transmitted by an animal host.
Most of these that list a rodent host are diseases in the wild rat population - not in pet rats. The only problem I have heard of between pet rats and humans is Strep or Staph infections, which can be a problem with any pet. The other problem would be allowing a child of that young age to play unsupervised with any pet. Animals will protect themselves from being hurt and young children don't always have good sense when handling animals. They can get hurt by poking fingers in cages or squeezing too hard when handling, resulting in a possible bite.