Two staff members told Glasgow Sheriff Court they were left "utterly terrified" of the man.
At the time he was a patient in Glasgow's Queen Elizabeth Hospital under the name of Arthur Knight Brown.
The incident happened after Knight was told he was fit to be discharged.
Dr Evelyn Millar said Knight, a wheelchair user, jumped out of bed and ran at her and nurse Yasmin Bagli.
He was found guilty by Sheriff Joseph Platt who stated that the witnesses gave their evidence in an "understated way" and "there was no exaggeration."
The sheriff added that claims Knight could not stand on his legs were "not credible".
Knight, of the city's Woodlands, was fined £400.
The American authorities have alleged that the man is Nicholas Rossi, who is wanted on sex charges in the state of Utah.
He claims he is the victim of mistaken identify and is opposing extradition.
Dr Millar told the court the man had become agitated after they told him he was going to be discharged from hospital that day.
The respiratory consultant said he became "very angry, very quickly," got out of his hospital bed where he had been wearing an oxygen mask and moved towards them at rapid speed.
"He was inches from our faces," she said. "We were just utterly terrified. We thought he was coming to harm us. It was extremely frightening."
Another witness said she locked herself in a different ward for her safety after the incident.
The charge against the man lists his name as Arthur Knight but says he is also known as Nicholas Rossi - the name of the suspect wanted by authorities in Utah over rape charges.
Court papers state that Knight goes by other names such as Nicholas Alahverdian, Nicholas Brown, and Arthur Winston Brown.
He is stated to be on bail facing extradition to the USA.
Knight has been stated in court as being a registered sex offender accused of other crimes including fraud and sexual battery.
The man in the court was in a wheelchair and wearing an oxygen mask, mirroring his appearance at previous court appearances.