On the actual mistake
The translation isn't as bad as others I've encountered.
A simple "nicht" ("not") added at the right place makes it a valid (although not accurate) translation:
"Die verlogenen Medien", so der Milliardär, "geben ihr Bestes, um einen Stern in einem Tweet zum Davidstern zu machen und nicht zum Sheriff-Stern oder ganz normalen Stern."
It can be an honest mistake and actually triggered my head-internal auto-correction: I read it as the corrected form and just noted a missing "nicht". Reading lots of low quality texts in different languages kind of hardens you for something as simple. It also carries no connotation making a simple mistake very likely.
More into details
I would see "Die verlogenen" as a somewhat inaccurate translation of "Dishonest". "Unehrliche" much better captures the degree of dishonesty, which Trump accuses them of. Sad to say but this translational mistake carries connotation and could be more than a mistake. While we established that the translation is not good, this can be seen as actual dishonesty. It's still not a lie though. They just overstated their opponent's position. I guess that's a stone Trump (or any politician for that matter) shouldn't be throwing.
For the original media text
Mit einem Stern vor Banknoten, der dem Davidstern ähnelt, wollte Donald Trump seine Rivalin Hillary Clinton als korrupte Politikerin darstellen.
"der dem Davidstern ähnelt" should be translated as "which resembles the Star of David". It's not like they are depicting anything that isn't there. They state an obvious resemblance. The only difference I can make out is that the Star of David is usually just lines and no filled area.
If Sheriff's Stars have six pointy corners, straight edges and are oriented (see text orientation) to rest on a single corner, they do resemble the Star of David, too. I remember Sheriff's Stars with five or six corners, which have small balls instead of points. Those with six corners may still mutually resemble the Star of David and the depicted star.
On one hand plain stars are usually five-cornered, straight-edged and stand on two corners. At least that's the most plain star I've seen yet. Plus it doesn't beg for misinterpretations.
On the other hand it could be plain (like "just") "any star with 6 corners" instead of any "plain star". That would actually make more sense than a Sheriff's Star.
Who else sees the connotation of "Fairytales fabricated."?
(Hi)story => German "Geschichte" =>
"Geschichten" => Fairytales
made (up) => fabricated