Well I asked for that. I should have said it differently. Another try: there is a lot of experimental evidence to show that the fine structure constant is constant. If it hadn't been constant we would have known. With the claim that the fine structure constant is a real constant one is on solid ground.
Then the possibility that outside of the solid experimental proof the constant could still vary "maybe the constant was not always the same" - should be handled very sparingly. It's an idea to be kept on a short leash because it's speculation. And often its untestable speculation , and it's best to stay out of that territory. And when you do experiments and they don't come out right, the hypothesis that 'maybe current scientific understanding is wrong' should be considered a very expensive claim that should be postponed until all other options have been exhausted. Instead, and partly because of popular media, it's become a very cheap claim that is easily made.
In the OPERA experiment they came up with the explanation that maybe neutrinos go faster than light. If you want to claim that maybe all of our scientific understanding is wrong then you need an awful lot of evidence to back it up, or you shouldn't make the claim. The guy should just have shut up and kept searching rather than hoping for a scoop.
People should not start trotting out a 'variable constant' hypothesis because some ratio of elements is wrong in ore.