So...
... I challenge that it is up to the receiver/hearer to take what they want from what someone said.
In some cases, yes (e.g., a random conversation at the park). But there are cases that are pretty clear-cut: a blog that consistently updates the world on my-incredibly-gifted-child is vulgar and bragging, whether the gift is for academics or sports or whatever. So is calling the newspaper constantly because Junior threw the winning pass again or whatever.
Honestly, I think reactions like Ms. Slaton's come from insecurities and the fact that people who are cognitively gifted have advantages that other people don't have. If you're a gifted athlete and you get injured (common problem), your career may be over and you may not have a lot of other options. Outside of brain injuries, gifted people have seemingly endless options.
This doesn't mean that we have to hide our abilities, but it also doesn't mean that people should just shout them out constantly. This kind of high-profile bragging just makes it harder for everyone. Remember, I'm only talking about people who look for any excuse to announce Junior's latest accomplishment, not people who are responding on-topic in a conversation or trying to advocate for their kids!
