I've had airport screeners (in Europe) try to do this to me on three separate occasions - twice in the UK, once in Germany.
On the first occasion I asked the screener to show me the rule that says that unmarked plain bottles aren't allowed. He relented ("I'll let you through this time"); I subsequently wrote to the airport authority who wrote back confirming that the screener had been wrong. (I have been carrying this letter with me ever since).
Similar dialogue on the second occasion (in Germany), screener relented ("I'll let you through this time") when I showed him the letter from the UK airport but still insisted he was right. Another letter of complaint, another - this time from the German Ministry of the Interior - again confirming I was right. That letter now lives in my travel wallet as well.
On the third occasion - at LCY - it took several email exchanges before the airport finally conceded that they had been wrong.
AFAIK there are no rules about unlabelled bottles, on either side of the Atlantic.