UPDATE: Talked to a Craig at the Florida State Parks. He told me that the volunteer was wrong. That the Ranger there was just "filling in" and she was wrong as well. We should not have been told to go back under those large trees if we felt unsafe there. He said that we could have stayed in the day use area overnight (during the storms) if we felt safer there. He assured me he would review the rules with the staff and volunteers.
PS: We had no problem with the camp hosts there. They were very nice people.
PSS: From now on we will be asking campsites about large trees (before booking) if the weather forecast is calling for high winds during our stay.