Conformance testing and the XML-test-suite

In the conformance test suite published by the W3C, there is a document 
that explains each test and the expected message/behavior of a 
conformant parser [1]. The section "Invalid" reads:

 > All conforming XML 1.0 Validating Processors are required to report
 > recoverable errors in the case of documents which are Invalid. Such
 > errors are violations of some validity constraint (VC).
 >
 > If a validating processor does not report an error when given one of
 > these test cases, or if the error reported is a fatal error, it is not
 > conformant. If the error reported does not correspond to the problem
 > listed in this test description, that could also be a conformance
 > problem; it might instead be a faulty diagnostic.
 >
 > All conforming XML 1.0 Nonvalidating Processors should accept these
 > documents, reporting no errors.

Is this accurate? I thought any parser-- including a non-validating 
parser-- could report violations of Validity Constraints insomuch as 
they can recognize them [2].

[1] http://www.w3.org/XML/Test/xmlconf-20031210.html#invalid
[2] http://www.w3.org/TR/REC-xml/#proc-types

Thanks for any clarification...

Jeff Rafter