God, how desperate I am for something to upend the standard model (imagine a person in a lab coat praying those words). I'll take anything that will push us towards a testable grand unifying theory.
I think this could genuinely be physics beyond the standard model. Even if it's confirmed with the remaining 94% of their dataset that they're still building, the only real impact I can see is quite a few string theorists out of a job. But it might unlock some physics that we could use to understand e.g. the early universe, event horizons, and other extreme regimes. When Gran Sasso was like "eyyyy guys, we got faster than light neutrinos!", that was a "no you don't, check your setup aaaaaaaaaand there's a loose cable" situation. This is not that. It's an entirely separate team of people refining and reconfirming not-yet-understood physics from an earlier team. Here's the announcement seminar: I'd love to talk shop with those guys. It's funny that I work in such a different branch of physics, but our lab setups are eerily similar. Ugh. I miss lab work.
I'm not a physicist or even a very smart man... but in this experiment, they did the math, knew what they were testing for, expected to see specific results... and didn't get those results. To an outsider, it looks like they went about the project in a slightly wrong-headed way, in that they set up a test to prove what they thought was true. Which is not how science is supposed to work... you set up a test that creates the conditions in which your hypothesis could be proven correct; not a test designed to confirm a specific expected result. So when the test didn't do what they expected, it is even more surprising. (If I am understanding this correctly.) So I'm thinking faulty instrumentation, wonky data - i.e. the usual suspects that defeat some scientific hypothesis - is not the cause of this unexpected wobble. Smarter people: Correct me if I'm wrong in any of this, please!