From what I understand, there are multiple factions of dragons, and each one has their own ruler. She is the Queen of the Silver Dragons specifically, but the school caters to nobles and royals from all the different factions
Asking that last question was smart, it was an honest question and relevant to something recent, and it would look odd if the one that answered yes to having issues in the relationship to not ask anything. It was an improvised move, but it sold the bit as a lot more genuine than it is.