Experimental evidence a photon can spend a negative amount of time in an atom

Here's my layman's understanding:

When light is transmitted through a transparent material, it slows down a bit. One way to think about this is that photons are being absorbed by electrons in the material and quickly emitted again to continue on their way.

This doesn't tell the whole story. For example, it doesn't explain why the photons appear to keep travelling in the same direction after being absorbed and re-emitted.

The overall delay experienced by a group of photons in this way is called the group delay.

But the atoms and the atoms' electrons aren't completely passive in this situation. The atoms can be resonating (moving back and forth) at a particular frequency determined by the properties of the material.

If the frequency of the atomic resonance is slightly faster than the frequency of the light (?) then the emission of the photon can happen at a time and place that seems be before the photon was absorbed.

This is not especially unusual for quantum systems and once again we get a headline that sounds absurd but only if you think about things classically.

No doubt my explanation is wrong/not-even-wrong/misleading. I would love for a proper physicist to enlighten me!