It certainly was true in our case. I traveled to Vancouver, BC for the fair (around 1985) with my then 11-year-old daughter who I'd raised alone since she was 19 months old. I had nothing to prove she was my daughter but after questioning us courteously for a few minutes and convincing themselves of our legitimacy, Canadian Customs officers waved us on. They could have detained us but chose to be neighborly.
Border agents on both sides are on the lookout for children being transported by non custodial parents or other non-custodial adults. I appreciate this policy.