The issue, which stems from laws preventing interlocking boards between companies that compete with each other, attracted the attention of the Federal Trade Commission earlier this month.
Some commentators suggest that Schmidt's handling of the matter, which he could readily resolve by stepping down from Apple's board, will show just how willingly he - and by extension Google - will be to compromise.
Schmidt's leadership experience was forged in the 1990s in Microsoft's aggressive pursuit of market dominance, when he was beaten first as chief technology officer at Sun Microsystems and then, as Gartner's Austin puts it, was "flayed" as chief executive of network software maker Novell.
In contrast to Microsoft, where then chief executive Bill Gates's aloofness and dismissiveness seriously harmed the software company's antitrust defence, Google is careful to cultivate a kinder, gentler image of Schmidt and the company's founders, Brin and Page.
Austin, however, argues that Schmidt is far from a political or commercial naif.
"Ever since Schmidt came in they're showing a very high degree of what we've referred to as adult supervision," Austin says.
"In other words, there's really strategy and planning and scheming and so forth going on there now.
"It's like guerrilla warfare. Guerrillas can attack with a small band and inflict major casualties on a very large organised army."
Most famously, Google successfully bluffed a multibillion-dollar auction of unused analogue television spectrum in the US two years ago to engineer an outcome that best suited its own products.
Legitimately, Google bid up the price for a key portion of the spectrum to ensure that the US government would require the winning bidder, Verizon, to provide an open access network. Open access networks prevent carriers from charging fees that grant priority to certain traffic, and proponents of the structure argue it maintains the free flow of information.
Network operators accuse Google of pushing costs back on infrastructure owners and have also accused the search company of being a "bandwidth hog".
Precursor LLC, a research firm backed by AT&T and Verizon, issued a hotly contested report last year saying Google consumed 21 times more bandwidth than it paid for, leaving consumers and other businesses to pick up the tab.
In the case of the auction, Google had no desire to own the spectrum, but its $US16 billion in cash meant it could hold up its end of the bargain if the bluff failed. It's an approach that Austin describes as a "Trojan horse strategy", and it's one that the company's dominant position in search enables.
It has also left competitors wondering, as Google's interests and product lines broaden, which of the numerous plays are truly important to the company.
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