They likely went through an ACGME residency. Many (maybe even >50%, can't remember the exact figure) DOs go ACGME over AOA. Does not matter for shadowing purposes. Chances of them being not board certified are slim.
The consensus is probably that ACGME is 'better' than AOA, but there are many variables at play. ACGME is the MD affiliated side and thus has pretty much all the academic teaching hospitals in the country. These are often located in bigger cities and get a lot of cases that smaller regional hospitals won't get or can't treat. They also have a lot more slots available. AOA doesn't have enough slots for DO graduates, so that's another reason so many go ACGME. I'll stop there as your question is a 'can of worms' scenario, but if they're board certified, ACGME or AOA, there's a near-100% chance they're a competent physician.
Search for 'residency merger' in the DO forum for information on the current goings-on regarding the two.