I think this is the part you are downplaying and which explains why they would want to avoid the PR. Although I agree with you it's a mistake on their part.
That call was THE biggest reffing blunder of all time. Comparing it to other reffing mistakes, like last year's Super Bowl, doesn't carry weight. It's universally regarded as the biggest mistake in sports history, no hyperbole.
The only thing I can think of, off the top of my head, that comes close is Jim Joyce's blown call that took away Galaragga's perfect game. And while a perfect game is one of the rarest feats in sports, in the words of Paul Allen, this isn't Detroit man it's the Super Bowl.
It's the most popular sport with a berth to the biggest game in sports on the line. And there was no subjectivity to it. It was wrong. And while I agree that the NFL normally operates on an any press is good press model, I just don't think they want any part of reliving that moment and it being relitigated (court of public opinion, not actual) all over again. That and I do think Bill setting foot in the Superdome will be problematic.
Now, I agree they are making a mistake. You handle it the way MLB handled the Joyce-Galarraga situation.
But, the NFL would NEVER acknowledge that error like this. So, c'est la vie.