It doesn't ascribe words to anyone. For the rest, yes, that's what political analysis is. Do you find all political commentary illegitimate or just the stuff you don't like?

"Putting words in someone's mouth" is different. It means ascribing a quote to them that they didn't actually say. It doesn't cover all speculation about what people think.

Pedantry - claiming ideas in other's heads is not much different.. That kind of 'political analysis' is similar to playground taunting - "you so stupid, you go gaa gaa gaa!" while making faces. Too shallow, broad and general to be useful as anything but rationalization.

Feel free to write your own analysis of the original question!