I'd guess it comes down to what counts as "the government."

Millions of people work for the federal government, and millions more for state and local governments. Is there widespread corruption among them? I don't think so. And I don't think my countrymen think so either.

But "the government" is often meant as just the very top. The President is corrupt. Big swathes of Congress are corrupt. We have a Supreme Court justice more or less openly accepting bribes. Among that small group, I would be comfortable saying that corruption is widespread.