The line about wheated Old Forester was only partially facetious, but I was unaware that one distillery would be working with the requirements of another distillery. That's something that does not come readily to my mind in this era of trade secrets.
Plus, I was under the possibly misguided impression that during Prohibition those who were selling brands would just be bottling whatever they could get their hands on and selling that as their brand. IE, Brown-Forman bought Early Times in 1920-something to get their stocks of whiskey; I just assumed that they were selling Early Times distillate as Old Forester so that they could keep the trademark alive.
Sort of like when a distillery (say, Wild Turkey) augments their stocks by buying in from another distillery (say, Buffalo Trace); they aren't buying whiskey that was made specifically to their specs, although the specs may be close enough to match. And the BT distillate becomes Wild Turkey even though it wasn't distilled at Ripy.
To a certain extent you are correct in your beliefs. The distillers were purchasing whiskey from other companies to keep the brand alive. They were also bottling whiskey for companies that had thir brands in the consolidation warehouses and simply charging a storage fee, a bottling fee and a small sale commission.
For example: Stitzel sold Henry McKenna brand during prohibition. They never owned the brand or the whiskey, but the McKenna's had their whiskey in Stitzel's warehouse. Stitzel (and W L Weller and Sons since they were sharing the license) would sell Henry McKenna at a sales fee of $1.00 per case. Stitzel charged the storage fee for the barrels and the bottling cost (material and labor) out of the sales as well. The McKenna's ended up with about 55% to 60% of the money.