Heya Andy,
These two options are indeed education-related, but education and career does NOT have to be mutually exclusive! Being an attending is a part-time thing, BUT it CAN be career-related, i.e. it's a great thing to do to supplement your career as a private dentist.
If you want to do it as a full-time career hospital dentist, then you will have to become faculty of the institution and take on teaching positions such as the program director of a General Practice Residency program or such. You will have to be at the leading edge of the profession though that's for sure.
VA Hospitals do indeed hire general dentists to do general dentistry and not (just) for teaching purposes. Those who do should expect to do A LOT of removable prosthodontics though! 😀 Most VA-employed general dentists prefer to work only part time rather than full-time because the full-time pay isn't quite as good as private practice, but yeah you can make a full-time job of it if you can't find any associateships to your liking (i.e. better than nothing).
Also, general dentists are needed as well at institutions that care for special-needs patients (i.e. mentally ******ed, patients with psychological disorders, etc). There are dentists who are altruistic enough to work for those institutions full-time and take the pay hit.. However, I suspect most dentists wouldn't touch that with a 10-ft. pole. 😛