It is beyond the purview of none but those who are lawless. If that was their ruling they should all resign. Disband the FEC.
You guys are both missing the point — for a change, we have a government agency who made the simple determination that they don’t have the authority to make a decision. By the laws and regulations as written, they have to allow anyone who follows the proper guidelines to file for and run as a candidate. They simply do not have the authority to deny someone on the basis of eligibility, because Congress has not given them the power to do so.
The main problem with the whole eligibility issue is that there is a Constitutional requirement, but no defined mechanism for enforcing it. Since Congress is the ultimate judge of Presidential elections, it is therefore their responsibility to provide for the enforcement of that requirement. If they do not delegate such authority by law to an agency like the FEC, the FEC would be violating the law and the Constitution by taking the responsibility onto themselves.