It's hard to answer this question definitively, as I suppose that some monarch somewhere in Europe could have demanded not to be questioned, but I have literally never come across this in any of my research (and I work on kingship). Here's a quote from Jean de Joinville's vita of Louis IX in which somebody asks him a question:

The prior of the hospital of Ronnay greeted the King, and asked him if he had heard lately from his brother, Count d'Artois. "Yes," said the holy monarch, "I know that he is in Paradise."

So I guess that's one data point against that claim. There are other things I can think of that would probably result in evidence of questions. Henry VIII's attempts to divorce Catherine of Aragon, for example, resulted in a trial in which both the king and queen were probably asked questions.

The book to go to about rituals surrounding kings in Medieval and early modern Europe is Sergio Bertelli's The King's Body. I don't recall Bertelli discussing a prohibition on questions, but there are plenty of other fascinating -- and weird -- rituals in there.