While I agree that politicians, commentators etc engage in double-speak and deception all the time, this seems to me a pretty clear case of 'asked and answered'.
Psaki response was that the questioner was just repeated a claim already made by Lavrov. So is that true? Yes! And had US Gov already responded to the question? Yes! Here:
Transcript of US DoS press briefing:
QUESTION: Can you say which ones – which ones of the claims – or just to give us an example of the --
MS. PSAKI: Which ones of --
QUESTION: -- of the claims that the foreign minister made in the interview that you would regard as quote/unquote “ludicrous”?
MS. PSAKI: Well, one was certainly that the United States has anything to do with Ukraine’s counterterrorism operations, or that --
QUESTION: Or that you’re running the show? Is that the --
MS. PSAKI: Or that we’re running the show or funding it, exactly.
MS. PSAKI: I would put those all in the ludicrous category.
So there you go, an unambiguous denial. Of course anyone is free to reject the answer, but they can't say a direct answer hasn't been given.
I think a good question for Russia Today (who uploaded the video and whose reporter is asking the question) would be: was it just a coincidence that their failure to report that the question had been asked and answered in a previous press conference ended up giving the impression that the question hadn't been answered at all, or did they misreport it on purpose?
Like I say, I'm no fan of Government spokespersons, but it's ironic when the people criticising are at it themselves. ;-)