MLB dropped the ball on this. He said he would take a DNA test to prove that the test wasn't his. If MLB let him take the test and he fails it's over and done and nobody would know about it. If he passes and it wasn't his sample then they are in the same boat as now. Most likely he would have failed the DNA test.
I had the same thought as you, so I asked somebody on a Cards forum about this and this was his response:
It's very likely that MLB refused because
1) They don't want to set a precedent for having to continuously DNA test all specimens taken throughout the process to make sure it's still the same person's specimen; and
2) They didn't want to give any legitimacy to the idea that this might not have been his specimen. By allowing such a test, they'd be saying "you know, we're not sure either."
Now, though, if they can get a de novo review in court, I bet they'd go for it.
There's a decent chance MLB appeals the arbiter's ruling in court. If they do that, a de novo hearing would be essentially doing the appeal all over again, except in court. The other option (not sure the latin on it lol) is for the court to just rule on the arbiter's ruling based on info presented (i.e. no new evidence).
Basically, I think MLB will look really bad if it's not Braun's specimen, but doesn't gain anything if they prove that it is. I mean, they'll gain legitimacy in that they didn't screw this up, but how much of the fanbase is going to remember anything more than "Braun won his appeal." The appeal is over, so even if they prove it was his, they can only gain something if it goes to a de novo hearing.