For certain definitions of "just fine". Some manufacturers will use a private tag to hold the same information that's meant to be in a standard tag—and even sometimes put different values in the two, with the private tag being correct.

Viewer of what? Dicom can contain other things than just nD imagery.

Also, the difficulty in my experience is the getting data back in part; getting data out is usually a lot easier (you don't need to care about those tags).