http://www.acgme.org/Portals/0/PDFs/Nasca-Community/FAQs.pdf
Under page 16. Appendix 1, question: Will individuals who are currently enrolled in AOA approved residency program be eligible for entry into ACGME accredited fellowships
Answer: effective july 1, 2016, eligiblity requirement for all fellowship positions require completion of prerequest training in a program accredited by ACGME, the RCPSC (candian) or CFPC (canadian).
Mind you, this isn’t from me. This is from the ACGME. Many fellowships are not ACGME accredited, perhaps explaining the source of your confusion.
You're missing the part where if the DO is coming from a pre-accredited (as in only a program that has applied for a ACGME accreditation - says nothing about whether they'll attain it) AOA program, then fellowship requirements are based on the 2013 eligibility requirements.
Yeah, that literally makes no mention of inadequacy of AOA training. You're extrapolating that. They made a policy change in order to "streamline" (read: take over) GME training. It was the best way to strong-arm the AOA without significantly screwing over ACGME programs (which is fine, I honestly don't care, and think the merger is overall a pro for the DO profession).
The point you're missing is what SLC and AnatomyGrey12 have said. ACGME fellowships were already taking AOA graduates. In fact they continued to do so, even when no programs had transitioned (agreeing to the merger MOU happened in 2014, but the first applications to transition didn't open until 2015). You can just as easily extrapolate the argument that since this was the case, it had little to do with the quality of AOA grads going into ACGME fellowships.
Now that too is an extrapolation. Unfortunately none of us can be certain, but our extrapolation and the belief that the merger had little to do with quality and everything to do with money and power is a bit more believable based on the facts than yours.
As I've already said ~50% of programs that have applied have already attained initial ACGME accreditation, ~17% haven't even been reviewed once yet (but its likely at least half will get accredited once reviewed), and again I wouldn't be surprised if another 25% that submitted managed to implement changes in the next 2 yrs to attain accreditation. The majority of AOA programs are able to get ACGME with basically no change, and another chunk need to make doable changes. This doesn't really paint the picture of most AOA programs having training below that of ACGME requirements that you seem to be implying throughout this thread.
Don't get me wrong, there are/were some really bad AOA programs out there, but be careful not to translate that into "most AOA programs are bad, and therefore most AOA grads have insufficient training".
EDIT: Also, to be clear, I'm saying this as someone in a university ACGME training program, so I have no dog in this fight. I just happen to come from a state with a lot of quality AOA programs. I also rotated at some that are now ACGME accredited and were in the process of doing the apps when I was there. Little had to change, they were already meeting the requirements, they just had to put it out on paper.