Does the distillery for bourbon barrel-aged beers really matter?

looking more carefully, the original post speaks of a brand (Pappy) & a distiller (Heaven Hill). realizing now, the question more specifically asks about distilleries - i answered above from a brand perspective.

 

I love Bourbon Barrel aged Imperial Stouts and fine this thread very interesting. It seems there is an assumption the better the Bourbon in the barrel was the better it would be for ageing beer. It could be that the barrels that aged the cheapest rot gut Bourbons are better for ageing beer than the Pappy Van Winkel barrels.