They can't say it's false until they've done a full investigation, which would require the kind of access to the pool that no news agency has.
Again, they can only say no evidence was provided for the claim.
Yeah, with the spork.
"Lying" implies intent. News agencies can't speak to the president's intent or what he's thinking or knows unless he explicitly states something. That opens them up to getting sued for libel.
That's why instead they said that the claim was unsubstantiated.