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.
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.