Branded products having recipes on the label has been a marketing staple in America for a long time. Sometimes you could mail them for a little book of recipes all using that specific brand of oil/chocolate/flour/etc.. Quite a few "old family recipes" are something that Grandma got off of a Crisco tin.

As another commenter mentioned, the various vinegar-based pepper sauces have a wide range of flavors from fiery (Tabasco) to piquant (Crystal). The Cajuns in my extend family use Crystal and Louisiana Brand sauce. These are more on the tangy side and have much less spice. Even my six year-old likes Crystal on his red beans. I've also seen a few purely local brands in their pantries. I've never seen Tabasco, however.

With hot sauces, there's a very distinct flavor difference between Tabasco, Crystal, Frank's, etc. not to mention there's regional affiliation to what hot sauce you use.

Additionally, I think a lot of "traditional" recipes in the US which were passed down in families came from advertising in the 40s/50s/60s, so they specifically call for "Hellman's Mayonnaise" or "Toll House Chocolate Chips" or "Heinz 57" or whatever.