Schmidt was elected to Apple's board in August 2006, a year after Google bought Android (and over a year after Apple started work on the iPhone). Unlike Apple, Google's smartphone ambitions weren't secret. Could they seriously expect Schmidt to file everything he learned about Apple's smartphone plans in an unmarked section of his brain that he didn't use when he was at his day job?
Techcrunch the day Eric Schmidt resigned from Apple's board:
"back in August 2006 when he took the seat Google had virtually nothing even remotely competing with Apple’s core products and services. "
http://techcrunch.com/2009/08/03/google-ceo-eric-schmidt-res...
2005: Android is a "mobile software company"
2007: Android prototypes look like blackberrys
2008: G1 launches as a iphone knock off with noticeable differentiation (horiz slider).
2009: Droid first high end Android smartphone, another horizontal slider
Jan 2010: Google releases a Google branded straight up iphone clone, Jobs flips out.
They were known at the time to be a re-assembly of parts of the Danger team working on a smartphone OS. To me, that's enough to know where Google's ambitions were pointing. The huge volume of "Google phone" rumors that started long before Android was unveiled says to me that plenty of other people saw that too.
I just don't see how, too anyone paying attention, "Google is working on a Danger-inspired smartphone OS" doesn't automatically imply "Google is working on something that could easily crash right into the iPhone."