The media speculation about why Eric Schmidt is ceding the Google (GOOG) chief executive role to Larry Page is “completely false,” Schmidt told a group of reporters Thursday at the World Economic Forum in Davos, Switzerland.

Noting that various pundits have guessed that his job shift from CEO to executive chairman was because of fears that Facebook had dented Google’s momentum or that Schmidt has clashed with Sergey Brin on China issues, Schmidt said the speculation has been wrong. Instead, Schmidt repeated Google’s previously disclosed explanation that the management reshuffle is about clarifying and tightening lines of authority among the troika that has jointly run Google for a decade.

“This has nothing to do with competitors,” Schmidt said. “I publicly said the next 10 years will be as successful as the past 10. We’re going to run this way for a while. It’s a full-time job just to deal with” the areas Schmidt will oversee, he said. These include “all the external stuff: customers, partners, deals, M&A, government, press, publicity and marketing. It was misinterpereted by many people who didn’t understand what I was doing.”

Schmidt characterized co-founder Larry Page, who will become CEO in April, as a brilliant products person who has participated in every major decision Google has made during Schmidt’s tenure. He said Sergey Brin, the other co-founder, will focus on “the order of three big initiatives,” on which Schmidt didn’t elaborate.

Schmidt also challenged the assertion that Google is locked in a competitive battle with Facebook. “We have a competitor called Microsoft (MSFT),” he said. “Microsoft has more cash, more engineers, more global reach. We see competition from Microsoft every day.” Facebook, on the other hand, “has clearly stated they don’t want to get into  the search business. Facebook users tend to use Google search. Facebook’s ads business does not displace our advertising. I’m somewhat perplexed by the obsession because I don’t think the facts support it. Things are going great for Google.”

Schmidt also took on Google’s competition with Apple (AAPL). Google partners with Apple, he said, on search, maps and YouTube. It competes, of course, on phones. Google also might in theory compete with Apple’s Macintosh computer business with its Chrome OS hardware that Google hopes “to announce later this year,” Schmidt said.

“Steve is absolutely brilliant,” said Schmidt, referring to Steve Jobs, CEO of Apple, where Schmidt was a longtime board member. “(He’s) the most successful CEO in the world anywhere.” Comparing Apple’s iPhone and iPad platform to Android, he said: “They managed to build an elegant, scalable, closed system. Google is attempting to do something with a completely different approach.”