Although not particularly well documented in this respect, the AssertEqualsTable routine only looks at the data in the table - not that the columns are the same. To check whether the table structures are the same, use AssertResultSetsHaveSameMetaData. I wrote a bit about this in this article.
You can of course run both in the same test, and the test will only pass if both checks pass.
I guess the reason for the split would be because there may be rare instances where you care about either the data or the metadata being consistent for your test, but not both.