But Mr Guiliani hit back: "No, it isn't truth".
Trump in a series of Sunday morning tweets is responding to a New York Times story reporting that McGahn has given hours of testimony to the special counsel investigating Russian election meddling.
"Yes", the president's lawyer insisted. Giuliani demanded, mocking Todd's facial expression. "Not the truth", Giuliani told Todd.
"I think this is going to become a bad meme", Todd warned Giuliani.
When the meeting between Kremlin-connected lawyer Natalia Veselnitskaya and Donald Trump Jr., Jared Kushner and Paul Manafort first came to light, the campaign claimed it was just to discuss Russian adoptions.
Giuliani, speaking on Fox News, repeated his concern about investigators' potential approach to a Trump interview. "Not the truth", Giuliani replied, as seen in the video excerpt from the Sunday program, below.
It was the moment when the phrase was coined that might be said to sum up the spirit of the Trump era: "Truth isn't truth".
Even Trump once told reporters Giuliani would "get his facts straight" eventually.
"It's somebody's version of the truth", Giuliani said.
Host Chuck Todd holds his head on his hands.
"He fired Comey because Comey would not, among other things, say that he wasn't a target of the investigation", Giuliani told Fox News' Sean Hannity. "Of course, any meeting with regard to getting information on your opponent is something any candidate's staff would take".
He pleaded guilty to lying to the Federal Bureau of Investigation and is cooperating with Mueller's probe.
GIULIANI: Yes, yes, each time by three or four days so we could write a letter in response.
Trump's legal team is still weighing up whether to allow the president to be interviewed by the special counsel.
Trump himself has also advocated a similar interpretation of facts, saying in a speech last month, as Inquisitr reported, "Remember, what you're seeing and what you're reading is not what's happening".