Apparently Eric Schmidt's time with Apple was filled with hush-hush inter-corporate agreements. The most prominent of those was an unofficial promise by both companies to not poach each others employees. TechCrunch reported on the issue, and claims to have confirmation from inside sources.
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This means that the Justice Department's investigation into the possible collusion between those companies had some ground. Schmidt's position as a board member of both corporations is said to have been the prime factor in these agreements. It's too early to tell if Schmidt stepping down will lead to an end in this practice.
TechCrunch also reports that there may have been some other 'agreements' between the two tech giants. It's rumored that Google didn't put multi-touch into Android because of a request from Apple, and Google has even admitted that they cancelled the Latitude app for iPhone in lieu of a webpage due to a request from Apple. The fact that Apple is working on a browser-based Voice app against Apple's wishes may be the first sign of these agreements breaking down.