Well, again, I'm not necessarily sticking up for them because I'm not them and for all I know, they're actually as mistaken as you say. But the concept of "weather is not climate" is a kin to "a data point is not a trend". Because weather really is climate, long term, and that analogy holds. Temperature drives air and water currents, influences gases, etc -- climate drives weather.
Because of this, I think it's not only reasonable but also likely correct to say that "ABC" was saying what I pointed out -- that a string of unusually hot days is part of the warming trend (by definition) and that an unusually cold day doesn't signify anything on its own. Nothing in what you quoted suggests that the previous statement -- that the warm days were part of the trend -- implies that those warm days suggest a warming trend. The warming trend is assumed in that instance (from other data and scientific consensus) and the connecting is, again, by definition. Saying, later on, that a single data point -- the cold days -- refutes the trend is nonsense, and that was pointed out in the statement "weather is not climate" (a data point is not a trend).
ETA: Man, I need to stop digressing so much! Sorry for the clarity issues above.