I have not heard that before. What I have heard is that if you do an allopathic internship that is not AOA approved then you cannot practice in Michigan, Pennsylvania, Florida, Oklahoma, or West Virginia.
No. Each state has its own licnesing rules, but none say that if you complete a DO residency you can't practice there. Try this website to alleve all of your licensing anxieties.
DO's are eligible for licensure in all 50 states. there may be some programs that are not accredited and, as such, do not set you up for board certification, but this is not necessarily a legal hurdle for practicing (assuming someone will hire you) since you will be licensed.