Fiat cannot be volatile because it wasn't created so. But you can use fiat as an investment or asset but not a store of value because an asset can depreciate or appreciate overtime.
Well in my opinion your statement is meant to be relative. This is basically because there are a couple of fiat currencies out there that are unstable and this is as a result of the nature of the economy of that particular country using that currency. The problem with so fiat is most inflation infact it's not just some it's basically a general problem.
The difference between most of them is that based on economic stability some fiat currencies get hit harder by inflation when relatively compared to others.