No, the woman kicked off the plane was quoted as saying that. How would she know whether the child had paid for both seats or not?
Just because YOU don’t know how the woman knew doesn’t mean she didn’t. If I had to guess, the stewardess explained the situation to the woman. Moreover, the reporter, who had talked to SWA, would have corrected the claim in the story if that were true. In fact, if SWA hadn’t confirmed it, the quote probably wouldn’t have shown up. Moreover, SWA wouldn’t be all that concerned about “apologizing” if the only issue had been bumping a full-fare standby passenger who complained and was rudely told to knock it off because the teen had bought two seats.
In all likelihood, the unpleasant discussion on the plane with the crew had to do with the fact that she knew that they had given the seat that she had a right to as a full-fare standby to the teen who had only paid for one seat.