You're arguing that we can ignore the entire actual content of the article, and blame reporters for the fact that readers might take their headlines alone out of context...
I'm arguing that most people do not read the articles, but merely look at the headlines. Do you disagree?
And as such, the media should be very careful about what they put as their headline. In fact, I think they already are being very careful about their headlines, such that their headlines are not the result of laziness, but are purposefully crafted.
So yes, they should be held accountable for their headlines.
Headlines don't have context, they stand alone. That's the point. To stand alone and grab your attention.
and at the same time we must give Trump the benefit of the doubt and strenuously interpret the context favourably.
Let's look at it like this: The "Stand Alone Principle". Does a sentence "stand alone" or is it part of a greater context?
If it stands alone: Then no, you don't need to evaluate the context
If it doesn't stand alone, but is part of a larger context: you need to evaluate it.
So since headlines stand alone, you don't need to evaluate the context in order to hold someone responsible for it.
Since sentences inside of paragraphs inside of speeches aren't stand-alone, you need to evaluate the context before holding someone responsible for it.
If there is context to consider, consider it.