I can't read this due to the paywall but I'm guessing it's based on Media Matters subscribing to the most extreme accounts and large corporations and then refreshing the pages hundreds of times until they finally got an ad to show up next to a post with "hate speech".
They may as well just have photoshopped the image for all the relevancy it has to the real world. Which is why X is suing them for defamation since X determined that Media Matters account was literally the only one that ever had those advertisements appear next to those posts.
Elon Musk is not suing Media Matters for defamation. Seriously, read the complaint. (Try searching for "cause of action".)
That's just as well for them, since defamation requires showing that the other party said something that's actually false - not something that's true but that presents facts in a way you dislike.
GENERAL ALLEGATIONS
II. Media Matters Systematically Manipulated the X User Experience to
Defame X.
III. To
Defame X, Media Matters Hid Its Manipulation from Readers and Advertisers.
SECOND CAUSE OF ACTION
Business Disparagement
46. Defendant Media Matters made statements that disparaged the quality of X Corp.’s product, X.
47. Defendant Media Matters made these statements as statements of fact, not opinion. Defendant Media Matters represented that X “has been placing” advertisements next to antiSemitic and racist materials. It represented that it “found” these materials next to advertisements.
48. As extensively explained above, these statements made by Defendant Media Matters were false.
49. Defendant Media Matters intentionally made these statements with clear malice, well aware of their falsity.
50. X Corp. suffered monetary loss as a result of these statements: companies mentioned in Defendant’s false and misleading article pulled their advertising from X indefinitely.
def·a·ma·tion
/ˌdefəˈmāSHən/
noun
the action of damaging the good reputation of someone; slander or libel.
Some synonyms for
defamation include:
Libel, Slander, Calumny, Vilification,
Disparagement, Denigration, Aspersion, Obloquy, Traducement, Blackwash.
If you want to split hairs, the exact charge is not defamation but "Business Disparagement". Regardless, a court will make the decisions of whether Media Matters was presenting something that was false with the intention of causing harm.