I think that if Emma and Henry shared a birthday then it would have had to be mentioned. Emma would have said something. Henry would have said something. It is our birthday. That isn’t something that can just not be mentioned. That would seem inconsistent. I have much less issue with Emma just lying to sound older when talking about when she gave birth because that seems like a normal lie and maybe she had been lying about her age at the time. I just have much less issue with Emma lying then with she and Henry sharing the same birthday.