Yes, it's falsifiable. If you cannot fit the model to the data, then the model must be wrong. That's the direction science technically works, but almost never how it is reported in the media. The fit here is considered a good thing, but cannot conclusively prove the model (as I think you are saying).

In principle, you could fit every single atomic/molecular spectrum to the data and falsify everything else based on some goodness of fit test, but no one does this.

Another thing about these molecular spectra is this: if there is an emission line missing, then it cannot be the spectrum you are fitting. These things do not change with environment, and can only be red or blue shifted due to special relativity. Every PAH spectrum must have the same lines. It's like a fingerprint.