Can a company simple change their "official statements"?

Google states that Google Public DNS does not permanently store personally identifiable information (source ).

However, imagine that in the future "permanently storing personally identifiable information" is exceeding advantageous. So advantageous that even after taking into account the kind of bad faith they will receive from changing their statements, they will still make a profit overall.

When that happens, is it true that Google could simply revert their statement and issue a new contradictory one? Is there some kind of law Google will have to abide to, which prevents them from doing so?

If they make a statement which they expect people to rely on, and people do rely on that statement to their detriment, then those people may have a good legal claim against Google if Google doesn't do what they say they're going to do. Further, in the US, the FTC would likely come breathing down Google's necks.

That doesn't mean that Google has to maintain that policy indefinitely into the future -- they just have to change the reliance. So, for example, publish that "it's no longer our policy, starting on day X."

The exact legalities vary country-by-country and state-by-state, and depend on exactly what Google promises.