The only official reference I've found to this situation is that VAT is due based on the non-discounted price on a prize gift. If you're a VAT registered company then of course it's not a problem as the VAT will be reclaimed.
Considering 100% VAT is only applicable on MRRP on "gifts" (Which I would say are of a personal and/or occasional nature) - typically given without any invoice, then it makes sense. (Oh how rude is it to give someone a gift with a price attached! shameful!)
Providing an invoice for whatever value you want (which is up to the seller, not the HMRC), and then adding a line for discount applied (even 100%) does not make it a gift. Also, samples are 100% VAT free. I would say a quantity of 1 is a perfect example of a sample. Luring a potential customer is what promotional samples are all about...
Realistically no VAT inspector worth his salt is going to waste time investigating whether these prizes are gifts/samples/100% discount prizes. Do they really want to take a battle up with Keysight on such a tiny volume of stuff? Especially when no actual money has changed hands in the chain?
Well we can all live in hope, if we get to win a prize that is.
Is that your opinion of what we'd all like to happen, or that of a tax accountant and/or HMRC?
As I said before if we could get away with paying no VAT by saying everything's a prize, we'd all be at it. While you might think it's noise on the accounting sheet in the big scheme of things, I don't know of any accountant who would squirrel away an odd item of non-trifling value, and the prizes are definitely that.
It's not a "sample" as it doesn't fit HMRC's description, punters aren't testing the product with an intention of making a future purchase.
On the other hand gifts are specifically charged at the full value, and is the closest official text that can find that reflects the scenario.
https://www.gov.uk/vat-businesses/discounts-and-free-giftsAs I said, we live in hope, but I am still glass half empty on the topic. If I picked up the phone and asked HMRC specifically the question, the answer is always going to be that VAT is charged, because that's going to be their default answer when they don't know. A reasonably experienced tax accountant would have a better view, in that if HMRC try to make it up as they go along, the accountant would be prepared to challenge the decision.
If you've ever had a VAT inspection, you'd know that you don't mess with the taxman. As soon as they find one suspicious anomaly, it normally points to other shenanigans, and they'll be over you like flies round a turd. I am sure that Keysight and their distributors will be aware of that.
But, as I say, we live in hope.