I just did more extensive testing of this on the VS 2005 RTM. In the sameple application you sent us, you displayed a document window containing a UserControl. The UserControl had a Button, a ListBox, and a ListView, each with their own ToolTip.
The Button and ListBox display tooltips fine. The ListView displays the tooltip ok over non-column client area but when displaying over columns, it shows and immediately hides.
I don't know what we could be doing to cause that so I created another test where I made a blank Form and put a ListView on it and populated it the same way you did. I applied a tooltip to it. This Form had none of our controls at all on it and exhibited the same behavior.
So the gist of all this is that we are not causing any issues with the tooltips. Any issues with ListView tooltips are bugs in the .NET framework itself because they occur when not even using our controls.
As an additional test, I went back to VS 2002 and ran the same sample. The tooltips display fine over any area of the ListView. This is definitely something Microsoft broke after the 1.0 .NET framework.