Here's what happens in 99% of duplicate seat assignment situations. "Excuse me you sit in my seat, here is my BP?" "Well, here is my BP for the same seat." "Oh, let's talk to a crew member about this." *people talk to crew member* *Crew member makes determination what happens next*
There is zero evidence this conversation ever truly took place. I have yet to see the person concerned clarify what exactly she said to the FA or an explanation why she simply let the other person sit in the seat her child was occupying.
The FA clearly was in a hurry and not fully aware of the situation. It's easy to simply switch to a likely and convenient explanation when distracted and in a hurry: "Oh there's a child sitting in his mother's lap, must be a lap child then" and may not even have checked her seat plan at that point.
Given the back and forth you often get with seats due to upgrades, no-shows, standbys, people switching seats 'unofficially' without asking, I bet it's far from uncommon on any airline - especially in short-haul with minimal turnarounds - that FAs aren't always 100% aware of whether the seating they see in front of them in the plane matches the manifest and instead have to rely on everything else having worked fine.