Larry--I may lack common sense, but perhaps not for the reason stated.
MCL 257.697, the Michigan statute governing signal lamps, including brake lights, does not prohibit flashing brake lights. 49 CFR 571, Section 108, the Federal regulatory code addressing brake lights and every miniscule aspect of motor vehicle lighting is also silent on the issue of flashing brake lights (at least as best I can tell).
If there is other authority to support the Plain Dealer's article on the Federal level, I have not been able to find it.
My intent is not to kill the messenger, but to determine the truth of the matter.
Keep in mind too, that although the CFR's may require manufactures to design and equip vehicles in certain ways, this does not prevent the states from enacting legislation as to modifications to the vehicle and its operation thereafter.