What fallacy or deception is this when falsely attributing a claim to the person making the claim when that person is not the primary source of the claim

I would say it is factual error, not a fallacy.  And, in one case, journalistic malpractice.

It doesn't seem to fit the definition  of false attribution.

I think there is an implied ad hominem here. The ad hominem being a veiled attack on the media.

The authorities and relevant evidence may suggest X is the case. The media will then report X. However, X may be inconvenient to a certain group A. It could make them uncomfortable. Undermine their strongly-held beliefs. Or perhaps sabotage their preferred political candidate.

Whichever way, they need to make X seem less believable. A tried-and-true way to do that is discredit the source; and by suggesting a (biased) media reported on it, it makes it seem as if they did so only to further their "agenda" - thus, X is not the case after all - or at least, we shouldn't believe it is.

P1) The media reported on X

Implicit P) The media is untrustworthy

P2) The media report on X is untrustworthy

C) We shouldn't believe X, or

C Alternate) X is not true at all

This is the ad hominem (circumstantial). In the case of the alternate conclusion, it is a genetic fallacy and non sequitur. Note that the vague and unsupported implicit premise gives the speaker a free license to dismiss all things that clash with their views as "untrustworthy media reports", while never applying the same scrutiny to things that the media reports which they agree with (selective scepticism).

It is also possible that I am jumping to conclusions and person 2 is simply mentioning the fact that the media reported on the President's remarks. I don't know for sure.