A Director's responsibilities
Schmidt served on Apple's board when he worked for Google. As such, he worked for Apple and it was his duty to serve Apple's interests, or recuse himself if there was a conflict of interest.
I don't know how much info Jobs shared with his board, but I suspect he was as tight-fisted with them as with the press, or even Apple employees beyond the few need-to-know on each project.
Google argues they bought Android before Apple made its announcement of the iPhone, and they may be right, but at that point it was a device more akin to a Danger HipTop, with a large keyboard, than the iPhone. If Schmidt got Google to switch to an iPhone-like direction on Android, he would indeed be in breach of his fiduciary duty to Apple, but it would be very hard to prove in court (but not impossible, see Oracle's success in proving deceptive intent wrt Android and Java).
I don't think Schmidt had necessarily that much control at Google. He was a stuffed suit foisted on Brin and Page by VCs with their inane belief in "adult supervision", and Brin and Page made sure he was cut out of the loop on many critical decisions, Android may have been. It is quite possible Schmidt mentioned something about the iPhone to Brin & Page, but that of course would be nearly impossible to prove.