Yes, although the products produced through Badge Engineering were not sold as the vehicle of a competitor:
Rolls-Royce Silver Shadow and Bentley T
Morris 1100, Austin 1100, Wolseley 1100, Princess Vanden Plas 1100, MG 1100 et al...
Jaguar XJ 6 and XJ12 as opposed to Daimler Sovereign and Double Six.
Most of the US output of GM, Chrysler and Ford divisions for decades.
The list is almost endless.
These days, things have taken a more sinister tone. Rivals and competitors are sharing platforms. Not just those within (for example) Volkswagen Group or PSA or Fiat Group, whom we know to be under large umbrellas, but rivals from completely different (and competing) corporate bodies.
The Ford Ka is a Fiat Panda under the skin.
The Opel Corsa has much in common with the Fiat Punto.
These recent trends are more akin to the sort of thing the OP is drawing to our attention and he is right to be concerned.
A secret organisation uses its foul practices to attract the senior managers of large corporations into its evil web of intrigue and world domination. It has existed for over 65 years and it is getting stronger by the day.
The saddle issue that the OP notices (for which well done, by the way) is just one more example of the devious and evil methods of this dark cabal whose name we dare not mention.
They now dominate the tobacco industry, the cheesecake industry, ice-cream, gin distilleries, fast-food outlets, the production of rubber grommets to soften the door-closing action on medium-priced family cars... Even budget coffees are in their toxic grasp.
Their web of evil extends across the globe.
I, for one, will be buying no more bicycle saddles. These people must be stopped. Ride standing up!