He said that he touched the man on the hip to steady himself and make sure he didn't spill a drink as he moved past him in a busy bar.
Jamie Harron has been in Dubai since July after having his passport confiscated following his arrest for touching a man's hip.
"I have advised them that they are at risk of being charged under the UAE's Cybercrime Laws for speaking negatively about the regime and that the coverage of this case should offer them some protection", said Radha Stirling, chief executive of Detained in Dubai.
Mr Harron, who had been working in Afghanistan, has lost his job and is said to be heavily in debt because of the case.
"When Jamie was called this morning by the police he was told that the case had been dismissed, and that he should come in to collect his passport", Stirling explained.
She said: "He nervously went to the police station today to get his passport, but he was anxious it was going to be a trap to re-arrest him". And while she praised Sheikh Mohammed's action, she added, "a fully functional legal system would not require outside intervention".
Ms Stirling said that his case highlighted a "urgent need for judicial reform in the country".
Jamie was sentenced to three months in prison on Sunday.
One of Harron's friends, British national James Allen, 37, who lives in Dubai, told prosecutors that the Scotsman bumped into the accuser's arm accidentally, sparking the argument, according to court documents.
He said Harron apologized to the accuser and "placed his hand on the side of his buttocks as a way of apologizing", according to court papers.
The 27-year-old from Stirling was arrested for alleged public indecency and drinking alcohol at the Rock Bottom Bar on July 15. It has the world's tallest building - the Burj Khalifa - as well as man-made islands, an indoor ski slope and miles of air-conditioned walkways in its high-end malls. It is legal to sell alcohol at licensed venues in the UAE, but it is illegal to be found drunk. Such laws are common in other Mideast nations, based in part on Islamic legal codes.
Around 1.5million British nationalists visit the UAE every year, with the FCO claiming "most visits are trouble-free". That's followed by a broad warning: "Laws and customs are very different to those in the UK".