First, thanks for all the research already done. I arrived here after eating a bag of Lay's crisps and noticing a reference on it to the "special SunSeed® oil". My mind sprang immediately to GM.
Then, there seems to be some confusion regarding the implications of a trade mark. A trade mark is just a mark, nothing but a name, so, unlike a patent, it does not imply an original product or process. You can register "WonderBlah" as a trade mark for ordinary water, and the registration will give you the exclusive right to sell water under that name, but the water is still just the same ordinary water that you can also get from your tap.
"SUNSEED" (the word itself, irrespective of capitalisation) is indeed registered as European trade mark number 004667821 by Frito-Lay Trading Company GmbH in Bern, in Nice classes 29 and 30 (various foodstuffs). In principle, Frito-Lay has the exclusive right to sell not only sunflower oil, but also a great variety of other foods and beverages under this name.
What is strange here though, is that "sunseed" is a widely used generic name for sunflower oil and generic product names are barred from registration as trade marks. In other words, you can't register "Coffee" as a trade mark for coffee, nor "Salt" as a trade mark for common salt. Or, if you do, you will enjoy no protection for the name against its generic use by anyone for the corresponding product.
So the question is: why on earth would a big company such as Lay's bother to register a trade mark that it cannot legally defend? Anybody's guess is as good as mine. Perhaps they thought that "SunSeed®" looks good from a marketing point of view and is well worth a couple of thousand euro registration costs, never mind that it's totally worthless from the trade mark proper point of view.