I'm unsure what she expected. We've heard the tape, she can't deny speaking of it. Saying to not to report it like that as that would be awful, is very naive.
a) It's probably true that having offspring gives one an incentive to concentrate the mind on getting things right for future generations.
b) I'm sure folk without children already have as large an incentive as anyone needs anyway.
As she is the one 'leave' camp candidate left it's rather disappointing she has allowed a newspaper to spike her reputation like that. Despite the issue being near insignificant. A lesson in not to get too comfortable in interviews and just saying whatever comes to mind.