Because, despite that she had a completely different opinion in the beginning, she has been able to "think" and to hear others opinion. This is a sign on intelligence.
Prince Philip has been shown stupid and egoist, from the beginning to the end. He had an old fashioned opinion, and during the whole story, he was fully stubborn.
The Queen tried to understand others opinion, and also, she behaviored in a way to satisfy her people's wishes, despite that she had another position. She is a Queen of a people, she has to try to "hear" people's wishes.
Considering the fossilized and for centuries old fashion mentality according to it she has been grown up, it looked impossible to behavior like this, but she managed.
For me this is an intelligent modern Monarch.
As for Tony Blair, he was clever and he saved the Monarchy this moment, but THIS was not the main point of the story...