Well, this ENGLISH speaker thinks so too... but there is a HUGE debate in another sample sentence discussion that boils down to "every lady is a woman, but not every woman is a lady". The point being that your answer MIGHT be correct, and hopefully is in most circumstances... but it could be terribly, horribly wrong too.
I understand your frustration, as this does seem inconsistent, however for an elision (the omission of letters in between words for those not deep into grammar/phonetics) to occur, it doesn't have to be the same sound. In this case it would be to simply smooth the transition. There's a few articles on the web about the use of the elision, but this does seem (to me) to be one of the few parts of Italian grammar that are full of exceptions.