Whether or not you purchase a seat for a child under two years old, the parent MUST hold them for takeoff and landing unless you have a car seat strapped in. It is very unlikely that a parent who purchased a seat would not bring a car seat to sit their child in.

The FA's would be violating FAA regulations if they allowed parents to seat their infant in a seat without a car seat. So this story seems like something is missing something. Is this soemthing the OP heard, or were they on the flight?