What you've heard is correct.
Sole parental responsibility is generally only ordered where there is a pattern of risk of harm to the child/ren in question, either through abuse, neglect or family violence. This includes physical abuse, as well as emotional and psychological. If a parent is found to be unwilling to support and encourage a child's relationship with the other parent, this is considered a risk, as well, and often leads to the other parent being granted sole parental responsibility.
Generally speaking, the court determines whether there is an unacceptable risk to the children according to the evidence, however I would argue the most influential evidence in family court proceedings is the credibility of the parents when questioned under cross-examination.
I don't like to give examples of what the court considers an unfit parent because it is determined on a case-by-case basis and depends on the judge allocated to your case.
Hope this helps.