An odd claim, since ABMI is not a licensing body, and a board certification is not required to practice medicine in Texas, where Dr. McCullough is licensed.
One might wonder how a body that does not grant medical licenses, and which has no power or authority to revoke a license in any state, might go about "threatening" the license of a physician licensed by the sovereign State of Texas.
Odd.
I think it is a viable threat. A formal withdrawal of Board Certification could likely be seen as a sanction of practice. That could become an issue at re-licensing.