As a player, someone sending me a screenshot of press would instantly make me suspicious of them. Sending a screenshot seems like someone trying too hard to gain your trust on the matter, especially considering they're so easy to fake (with Chrome, anyhow).
As a former moderator (mainly on vDip, but I was one here for some time too) I would not say that sending screenshots violates any rule, even rule #4. Rule #4 specifically states "Lying is fine in Diplomacy except when it gives mods/admins unnecessary work to do!", so this rule is only broken if the mods/admins are given unnecessary work. So what exactly breaks this rule?
1) Accusing someone (this includes yourself!) of breaking another rule, or hinting that someone has, when you know they did not,
2) Saying that the site misadjudicated, or hinting that it has, when you know it did not (bear in mind this only applies to saying that it was the site's fault; saying that you accidentally misordered doesn't break this).
The above cases both give the mods unnecessary work; the first makes the mods have to launch an investigation for no reason, and the second means the adjudicator is supposed to be looked into - although it probably won't be.
The second case obviously isn't being broken here. The first case relies on another rule being broken, or this being hinted at, and since there are no other rules that cover screenshots this part doesn't cover screenshots either.
You could argue that if someone did send in the screenshot asking for confirmation that it was true, that would waste mod time because they would have to reply. In reality this will be replied to in no time at all, just by typing 'Sorry, we can't tell you that - it's part of the game.' It's no different than if someone sent in some chat someone else had copy-pasted and sent to them and asked if it was true, or if someone asked if the orders France had said he was going to do were what he had actually put in. Lying is part of the game, and we're not going to confirm/deny what someone else has said, unless it breaks either of the previously stated cases.
We never really had any discussions about rule 4 here or on vDip while I was a mod, so this is only my perspective on it, not necessarily the one the mod team holds. However, it was always the one that made the most sense to me - interpreting rule #4 any differently makes the wording extremely ambiguous.