UA admitted their flight crew was utterly incompetent for willfully failing to follow their guidance on children over 2 must be in a seat. 

UA admitted the senior flight crewmember in charge failed to ensure the crew was competent, knew UA's rules. Knew to check with the gate agent in case of ticketing issues.

"Once infants turn two years old, they are required to have a purchased ticket and occupy a seat." https://www.united.com/web/en-US/content/travel/specialneeds/infants/default.aspx

UA keeps shooting themselves in the foot thanks to their clueless CEO.