What is the English term, when someone provides truthful 'extra' information in support to promote own propaganda?

Though the title asks the main question, I will give an example.

Imagine a tabloid, which wants to defame a famous personality, say Abraham Lincoln or Michael Jackson. The writers know that, just criticism won't be sufficient. Hence they provide some good & truthful information about them. Along with it, they also insert their own un-verified information which they think is correct.

In day to day life: In college, 2 friends have a verbal spat in front of others. 1 of them decides to defame other by wrong means. Hence he/she tells like this, "Though you might be a good student & sport person, what you have done today is unpardonable."
Now such statement will excite many against the receiving person, as the initial information given about him/her was true. Hence they tend to believe, that the remaining information also should be true.

Is there any English term for such entity or activity?

Edit:
According to this answer, half truth seems quite matching. However, above examples can be extended beyond single person. i.e. If someone prefers US Republic party over Democratic party, then they may say something like this: "Democratic candidates like Bill Clinton & Obama were greats! Hillary is no match to them." Or a person not having much knowledge about boxing can state like: "Muhammad Ali was amazing. Mike Tyson is nothing in front of him."

Here, it's "complete praise" followed by "complete criticism". There is nothing half-half. So even though, one doesn't like "Democratic" party, they praise its previous candidates to insult current candidate.

_{^{Note: If anything not clear, I would be happy to edit my question.}}

You could consider using half-truth that means:

A deceptive statement, especially one that is only partly true, is incomplete, misrepresents reality by telling part of the truth, or alters the time sequence of truths.

[Wiktionary]

Usage example:

Some forms of half-truths are an inescapable part of politics in representative democracies. The reputation of a political candidate can be irreparably damaged if they are exposed in a lie, so a complex style of language has evolved to minimise the chance of this happening. If someone has not said something, they cannot be accused of lying. As a consequence, politics has become a world where half-truths are expected, and political statements are rarely accepted at face value.

[Wikipedia article on half-truth]

Conflate: (verb) combine (two or more texts, ideas, etc.) into one.

Conflating of truth and fiction fits the situations which you gave as examples.