It seems to me that it comes down to how the day of the week was picked. If they picked a random day of the week, and there was only one boy, then there is onl

It seems to me that it comes down to how the day of the week was picked. If they picked a random day of the week, and there was only one boy, then there is only a 1/7 chance of a boy being born on that day. If they have one boy, who was born on a Tuesday, and that is why they picked the day, then there is a 100% chance of a boy being born on that day, so no additional information is conferred.