Thanks for the replies all. It's all pretty much in line with what I was thinking.
And then, while a couple of miles may not matter, does three, four, six? And you'll find different views from different controllers about what 'own navigation' means in terms of track-keeping performance.
LookingForAJob, this generates another question open to everyone. Consider a deviation from track centreline that will be more than a minor one - say, 30 miles or more - would it be better for all involved to ask for a reroute via a fix that is in the clear rather than asking for deviations? Does that make your lives easier or harder?