How important is the statement of purpose in a PhD application for admission to a top school in the US?
This is an extremely general question, since it doesn't refer to the discipline. Since another answer comments on the social sciences, I'll speak up for physical sciences. (I'm in chemistry.)

We look at every facet of the portfolio. To do otherwise is to ignore useful information on the applicant. Let's be honest, we don't have much data. We get grades, GRE general scores, GRE subject scores, and recommendation letters. Plus the statement.

I mentioned in my answer to another question that GRE scores will sometimes serve as a first screen, to cut the pile down to a level we can really analyze. But that's not a "tacit acceptance". (I don't even know what that might mean.)

Yes. After a first cut, we look at the statement of purpose 100% of the time.

And yes, if someone writes a lousy statement with an otherwise good package, it's a bad sign. It tells us that the student just doesn't care to do a good job. Is that someone I want as a grad student? Probably not. 

Even if a student has stellar grades, GRE, and a paper in Science but the statement is poorly written, I'm going to think twice compared to a student who might be a bit behind, but seems to have a vision and sells themselves well in the statement.