Are those other charts IPA? It's not clear from the links. I thought there was only one IPA vowel chart, and you couldn't move symbols around willy nilly. If you can move the symbols around, then obviously I can place [a] where someone else places [ɑ] and Bob's your uncle.
I feel like the whole point of IPA is being corrupted.
He still can't spell 'cat' /kɑt/ (Unless there's another chart that says he can and that has [ɑ] where [æ] traditionally goes. But wouldn't that be cheating?)