I'm not trying to go to bat for The Company but all sources of information "influence the media" and it's the job of a good journalist to get info from every source available to them, including intelligence agencies.
The wording of "influence" is just too vague - prohibitions need to be specific. The CIA saying they'll deport your undocumented housekeeper if you don't print XYZ is one thing, them feeding information with "spin" on it to a journalist is another entirely.
Spin is merely interpretation and framing. /You/ can de-spin anything you read when that's all it is and you should. Read stuff from biased sources that have a very different outlook to yours. Al-Jazeera, the BBC, NPR, PBS, even disasters like MSNBC and Fox are worth some attention despite their unbelievable amounts of spin.
Lies are lies. It's not framing. It's not interpretation. It's "Saddam Hussein has weapons of mass destruction."[1]
Spin that as we must go to war. Frame it as a global crisis. You can have a subtly or radically different viewpoint. When the majority of the country believe the deliberately planted lie, /spin/ is basically irrelevant.
Influence the media is more about publishing deliberately fabricated lies designed for a given purpose and treating them as fact. It can get a country engage its army to kill when it otherwise would not want to do that. Doesn't get much more serious and less like /spin/, imho.
[1] Or Russia pays bounties to kill American troops in Afghanistan and the President does not care. Exactly when the president is trying to execute policy (rightly or wrongly) on Afghanistan. It's not spin when it's a lie, treated as truth to mobilize public opinion where it otherwise probably would not go. Rightly or wrongly the American public overwhelmingly support the withdrawal from Afghanistan and did so under both Biden and Trump. For those who supported remaining in Afghanistan this should be a concern that such happens and seems not to have direct consequences when exposed. One indirect consequence is the increasing total mistrust of factual news reporting which is something of an issue in a democracy.
What is interpretation? What is spin? What is framing? There is such a thing as an incorrect interpretation. Calling my flooded basement a "global crisis" is simply wrong. If I know it isn't a global crisis and yet continue to claim it is, then I am indeed lying.
Spin involves deliberately misleading people in a way that suits your ends which is also characteristic of lying, or at the very least, it characteristic indifference to the truth (bullshitting) and concern for producing a certain desired result. Whether this qualifies under a strict definition of lying or not, it is nonetheless in the same general vicinity. Both involve the abuse of language by using it as an instrument of power wielded over another.
The wording of "influence" is just too vague - prohibitions need to be specific. The CIA saying they'll deport your undocumented housekeeper if you don't print XYZ is one thing, them feeding information with "spin" on it to a journalist is another entirely.