sorry but cannot see PADI response as a brush off. If she did not meet the requirements no PADI certification. It's that simple. Some credibility is lost by calling alternate air source "buddy breathing" as the skill of buddy breathing has not been a requirement for a few years now. If all reading, view of video,knowledge reviews, quizzes, final exam, pool and confined water was done correctly I would think it unlikely the wrong terminology would be used by the student.
Any instructor from any agency can withhold certification if the agency standards are not met. I had a student I certified once ask me to take on his wife, who was physically handicapped, as a student. I refused as I felt she would not be safe in water. She had both a physical disability and learning disability.
My former student did not like it, but she is not getting herself or someone lose hurt on my watch. They went to a HSA type instructor and she can only dive now to my understanding with a dive pro and another diver who is trained by their agency to assist her. They went on 1 trip on their own to Bonaire to get this certification, with this instructor who traveled from Pennsylvania to join them. She made the required certification dives and never dove again. Sorry but this was way out of my comfort zone.