Only recently has Willett released their own distillate (in the form of a new "Old Bardstown Barreled in Bond (which may well be Heaven Hill)), but yes most of their stocks if not all of it was distilled by others. Notably, most of their current stock is either Beam, Brown Forman or unsurprisingly, Heaven Hill (which is literally just across the way). As far as Johnny Drumm, Vintage XO, Pure Kentucky XO, Old Bardstown 101 go, they're all variations of Heaven Hill juice. Likewise Noah's Mill and Rowan's Creek also fall within that same category of being most likely heaven hill at different year intervals.
Though Willett's own distillate might have one or two barrels that are wheated, I do recall a few of their Family Estate Single Barrel bourbons recently being wheated mashbills, maybe it was barrel #1400? Certainly their C and B series and some of their older block letter 17-19 year 1993 Distilled Family Estate bourbon is wheated as that's confirmed to be Bernheim distillate. Ahem. Anyways if in doubt, it's most likely Heaven Hill.