“An XML document is valid if it has an associated document type declaration and if the document complies with the constraints expressed in it.”
This means that in theory only an XML document that has an associated DTD can be valid.
In reality also XML documents validated with XML Schema, RelaxNG and even checked with a specific application are seen as 'valid' XML.
So probably a better definition would be:
An XML document is valid if the document complies with the constraints expressed by an XMLSchema, RelaxNG, DTD or any other specific constraint checking application.