Getting into detail because you need to is a good thing. Getting into detail because you want to, because you can, because your background allows it, or because you reckon that you have more technical skills than the person who should be looking after the detail, is probably a bad thing. Knowing the difference is critical, and it is essential to be honest enough with yourself to know the real reason why you are getting into the details.
However... The above was written before David's edit, in which he asks for comment on intrinsic abilities. I'm no psychologist, but my instinct is that the great project manager needs to be focused on delivering against a set of agreed outcomes for most of the time. At the risk of mixing my metaphors just a little too much, from time to time this will require a rummage through the weeds to find out what is going wrong or to pick up the pieces, while at other times it will require a quick trip in the helicopter to make sure the forest is still more or less the same shape as it was when the project started. However, most of the time will be spent working with individual trees or small plantations within the forest, nurturing, protecting, felling, and extracting the timber as appropriate.
What I'm trying to say is that there is a difference between the role of the technical specialist, the role of the project manager, and the role of the corporate strategist or corporate leader. Some people clearly have the ability to carry out two or even all three of these roles, but they are fulfilling different roles at different times. But, as I say, I am no psychologist, and these are purely my views based on many years of observing colleagues, and taking an interest in trying to understand what works and what doesn't.