I think the term "accidental project manager" is overrated in this day and age. Many project managers are now hired from outside (because they have project management experience), and are not promoted from within.
The way someone becomes a project manager right now is no longer an accident, it's because that someone wants to be a PM. You have no idea how hot the question "How to be a project manager is?" these days. That means many people actually want to become Project Managers.
So yes, there are still some accidental project managers, probably more than other professions, but that doesn't mean that project management is an accidental profession, nor does it mean that project management is not a profession...