Remember basic Goverment 101 from elementary school? The Legislative branch makes law. The Executive enforces law. The Judicial interprets law.
Congress makes officers' orders legal. The CIC enforces their orders through the chain of command.
And that particular argument under cuts the hypothetical of there being mass military disobedience and chaos if Obama was found to be ineligible to give lawful orders; as that would be highly doubtful in any case.
Furthermore, there would be a political solution for an unconstitutional president, as the politicos of this country, would find a quick solution to the problem.