I read a good article about this a few years back when schools in Edinburgh were falling to bits. It pointed out one of the big flaws with Government procurement procedure is that if it falls to politicians to make the decision on a contract award - either directly or indirectly - they will always go for the cheapest option as they’ll never be rewarded for spending more than they need to.
There’s definitely no EU rules that implore public bodies to pick the cheapest option and I’d bet any politician who suggests so is either making shit up to a) piss on the EU or b) justify some shitty procurement decision they made in the past.