Yes but there are exceptions. Sometimes they even claim "Fake News" for things that they did personally release in a press statement.
To be fair, this was Mnuchin decrying something Trump had said, so it wasn't "personally".
Also, in this case, not the White House but the Treasury1 waving the "fake news" flag.
Not that it makes much difference. In my estimation, Mnuchin has dropped from "pretty smart asshole" to "pretty stupid asshole" since he was appointed.2 This looks like him shooting off his Twitter-mouth before checking what his boss had said.
1The Secretary of the Treasury is a Cabinet member, but Cabinet pronouncements are not generally considered to be "from the White House". That phrase usually indicates blather from the POTUS or his spokesbeasts.
2His career was, frankly, pretty undistinguished. Yeah, he did fine as an investment banker, but there are tons of successful investment bankers. He had executive jobs at Goldman, but at an organization like that, the executives are not the cleverest employees. He ran one successful clever scam, as far as I know - the rather nasty IndyMac / OneWest foreclosure-with-FDIC-rebates business. He bankrolled some successful films, and also some flops. And so on. As SoT, he's been a complete waste of space, with no significant accomplishments and a string of petty scandals and missteps.