I pretty much agree with you. Personally, I would not have said the word to the 11 yold.
We don't curse in our home, and my kids probably wouldn't have recognized the word at that age. Later, I did later make sure they were familiar with curse and a few derogatory words to avoid embarrassment, but I didn't drill them into their heads like their math facts.
And around here WT...could easily mean WTH or WTF, but no one would get WITW from it.