I should mention that the RzListView1.ViewStyle should be set to vsReport, otherwise no columns display (by design). But hopefully that was obvious.
Also, I just did a bit more poking around and discovered that it FillLastColumn is False, then it displays the columns. This appears to be a very old bug resurfacing. A work-around therefore appears to be setting FillLastColumn to False at design-time, then setting it to True at run-time. Not the greatest solution, but I can work with it for now.