Pricing an IR swap doesn't require any stochastic model but calculation of the PFE for an IR swap would require the Hull White Model or any other stochastic short rate or forward rate model.
Is this statement correct and if so, why?
A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future.
The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile rates are, the higher the PFE.
It's a bit like saying that the price of a portfolio of stocks does not require models, but the VaR does.
Fully support the prior comment. Swaps can basically be priced off the current Yield curve in an arbitrage free manner. The PFE as the name "potential" future exposure suggests refers to a value something (i.e. the swap) could potentially realize. Hence one needs to decide upon a simulation method to derive this potential value. The PFE as a measure of future (mark-to-market) credit exposure is often also referred to as the "Upside VaR", which is another hint in that direction, since VaR methods are usually also parametric (in the sense that price/value changes are assumed to follow certain distributions) or simulation based.