It's described here in more detail how it ended up being called the way it is:
http://ja.wikipedia.org/wiki/%E3%82%A2%E3%82%A4%E3%83%90%E3%83%8B%E3%83%BC%E3%82%BAto summarise:
1. The name originates from a Spanish name, therefore the correct pronunciation would be ih-ba-ni-ess.
2. in the main market for Ibanez (i.e. in English speaking countries) they were commonly reffered to as I-ba-needs or I-ba-nize
3. The Japanese read it in Roma-ji, and called it ih-ba-needs (dunno how, coz that'd be reading it wrong)
4. The Japanese thought it'd be cool to say it the same way as the foreigners so decided on I-ba-needs (or "ai ba ni - zu" in katakana). The pronunciation became official in Japan in the late 1980's
It's funny how they copied the English speakers even though they were wrong.