JimP,
No problem. Thanks.
I thought I would add another note to my original findings in the hopes of bumping this back up to attention:
If you right click edit shape and then right click again on the line between the points, you then get a popup which includes the option to 'straighten segment'.
This returns the line behavior to that of the original Word Draw (hard corners between vertexes) but only until you next move or change the line.


At which point all the vertex points become vulnerable to 'curviness' again.
Also at issue is the fact that sometimes right clicking will in fact -add- a point rather than bringing up the segment choices.
This is incredibly poor functional design.
If there is anyone out there with Office 2003 or 2007, does your Word Draw function work this way?
If not, I think I may try and source an older copy of Office from someplace.