Hiya Capt!
Based on my relatively short time as TC controller and reasonably recent indoctrination (sp?) at the college you are understandably a little confused.
If you've been assigned a heading and then told to 'resume own navigation DVR', theoretically you should take resume your flight planned route in the most direct route and then continue in accordance. It is a rather vague statement and open to individual's interpretation, possibly resulting in a relatively large turn.
Similarly if you're asked to 'route direct' or 'resume own navigation direct...' then you'd be expected to route from your current position to the point instructed. I think a vast majority of controllers would expect you to do this no matter how they had worded it. I certainly would.
The own nav instruction is usually a good indication that your precise track is no longer being used to provide separation from other a/c so any misunderstanding should not have any real consequences.
Of course, if in doubt, we'd always prefer you to ask for clarification rather than assume. Not so critical in this instance but the number of level readbacks where the pilot has obviously not heard clearly and guesses is quite scary. Then assumes the controller will correct them if they're wrong. Always a risky way of doing things!
Hope this helps, be interested to see if others would agree