RO versus distilled?

Everywhere I read and on here everyone refers to distilled as the only "safe" water to drink. We use a 4 stage RO unit so the kids can drink water out of the fridge dispenser. We changed the filters recently and they were dirty. So I know the RO is doing SOMETHING. The problem is my husband isn't too keen on buying a distiller since we have the RO unit. So am I doing harm to myself and my family still using the RO unit? Thanks, I enjoy reading your responses!!