Ex-FMCG Buyer (M&S, Tesco, Sainsbury, Woolworths, Homebase, PC World, Argos) chiming in. The larger retailers will have a mix of products going from (1) branded and own label almost identical apart from, say, packaging to (10) branded and own label bear no resemblance whatsoever to one another. Whilst its true that it does tend to be the same factories producing all of the product variants this is more to do with logistics and cost saving than any conning of the consumer.
It's very rare these days for supermarkets to use their own brand as a loss leader; that was definitely true in the late 90's where tomatoes sold for 4p a can but cost 21p-ish to the retailer to buy in. Not these days, though. Own brands are typically used to do 2 things : (1) appeal to those who can't or won't spend more and (2) push those who can spend more on to the branded or premium product.
Anyway, to answer the OP's point, I was once told by our Legal team at Tesco that there are actually no branded products which are absolutely identical to their own label counterparts. This is mainly to do with IP restrictions but also has elements of brand maintenance/strengthening and a ton of other stuff I won't bore you with. This does not stop certain own label items from being very, very close to their more expensive branded cousins, though. Product specification of products is a black art and even the slightest change to the make up of that product can be enough for it to be considered different to another almost identical item.
So, I rambled a bit there, sorry. Hope some of it was useful, OP.