Why did Jesse say that Winnie was the only person in the world to know Tucks' story in "Tuck Everlasting"?

Although Miles warns that "there might be a whole lot of others, for all we know, wandering around just like us" (Chapter 8), the Tucks have been very careful not to tell anyone about the magic waters, because they feel that to do so would be dangerous.  They know that

"If people knowed about the spring...they'd trample each other, trying to get some of that water...that'd be bad enough, but afterwards - can you imagine?  All the little ones little forever, all the old ones old forever...the wheel would keep on going round...but the people wouldn've turned into nothing but rocks by the side of the road...'cause they wouldn't know till after, and then it'd be too late" (Chapter 12).

The Tucks know that the idea of living forever sounds really good at first.  It did to them, until they realized what it really meant.  Now, deprived of the possibilily of growing, they are stuck in a sort of limbo; cut off from life with all its passages, their existence is aimless and isolated.  The magic spring is on Winnie's family's land, and she has stumbled upon it by accident.  It is to prevent her from drinking from it that the Tucks have had to tell her its secret.