This is pragmatics. Yes cool has multiple literal and metaphorical meanings. But only one is understood when the sentence is read in context: The meeting was unfriendly.
We know this from lots of clues: There is a co-location "warm reception/cool reception" these words go together idiomatically to give a particular meaning.
"Cool" meaning fashionable is still rather informal, and doens't match the newspaper-like tone of the sentence.
Reception here means the greeting that the PM received. The sense of "fashionable" doesn't seem to apply to the manner in which two people greet each other, but the sense of "unfriendly" does.
The context of senior political leaders, usually old men or women in suits, and a formal context: welcoming a political leader to a meeting. This means that being fashionable is irrelevant, but the friendliness of the reception is relevant.
When understanding any language, meaning is always understood in context. And the context here only permits one interpretation. No cognitive dissonance.