I don't think "I felt sad" represents any particular function. That's not really what the functions are/do.
The thing about inaccurate representations of global warming sounds like Ti. ("This is not consistent with what is realistically true; therefore, it is not compelling.")
I think Fi is more likely to pity the polar bear anyway because he got screwed through no fault of his own. Failing to empathize because they got the scientific facts about global warming wrong doesn't sound very F at all.