I believe you are correct about it being Nadeshiko (first time around) instead of Natsuko... Natsuko is usually Kanji'ed differently: 那津子, 奈津子 or 夏子 (in no particular order).
First time around? Actually, my first edit about Natsuko was in response to the user named cremefraiche since they tagged it Natsuko instead of Nadeshiko. After digging around to find any basis, I decided to step in and change the tag from Natsuko to Nadeshiko.
Seems I added the tag at the same time you wrote your comment, so I missed it. To my knowledge Natsuko is a valid reading for 撫子, but I guess you are right. Since Nadeshiko is more common that's what should be used. Oops.
