I'm Italian and agree with you. This said, I'm reasonably sure that in countries like Brazil ciao is only used as good bye, so maybe this explains the confusion. FWIW, I've also saw it written as "chao", which made me rofl.
The word has been incorporated into other European languages with spellings that make sense for that language. Other commentators have mentioned the Portuguese, Spanish and German forms. To add to those, I've come across "Čau" in a number of Slavic languages.