3 sigma is termed "evidence" in particle physcis (while "discovery" is reserved for 5 sigma) and is often enough to get people interested. Keep in mind that these are just numbers and must be interpreted in context. There have been tensions in various heavy flavour measurements for a looong time and across multiple experiments. It is very plausible that this is where we'll finally see new physics at the LHC. So it is worth serious consideration.

The super-luminous neutrinos had 6 sigma significance and still no one took it seriously because it was simply such a ridiculous claim. Obviously the number of zeros in your p-value don't mean a damn if you haven't plugged in your equipment correctly!

Indeed, there have been 3sigma deviations before (e.g. the diphoton resonance) which attracted a lot of attention and turned out to be nothing.

I'd encourage people to read up on the Look-elsewhere Effect when you see something like this:

https://en.wikipedia.org/wiki/Look-elsewhere_effect

I'm not saying this isn't potentially an interesting result, but 3sigma deviations when your parameter space is so large is actually not a big deal.