Does something in full-fat dairy actually protect the heart, or is it that people replace diary with margarine, which damages the heart? Are they able to separate out people who reduce dairy consumption without a corresponding increase in margarine consumption?

You're absolutely right about drawing inferences. Scientists have been doing that with the best of intentions for decades and they've been consistently wrong.

It's not easy to test, even under controlled conditions. You can replace one item with a different item, but you can't just eliminate an item without replacing it, or you're also reducing calorie intake. Then how do you know your results aren't due to the caloric change?