Emergency services were alerted and the Burrowhead site, near Isle of Whithorn, was sealed off.
However, local sources say the man was found to be armed with nothing more dangerous than a water pistol.
Shocked holidaymakers were advised to stay indoors until the police operation was over on Saturday.
Residents of the quiet seaside haven were shocked to see police cars and ambulances tearing through the village heading for the scene.
Others, who heard that the road down to the holiday park was closed off, assumed that a farm had been hit by a contagious disease like foot-and-mouth. Farmer Peter Simpson, of nearby Cutreoch, said: "As far as I know, there was a hoax call to the police from some guy who said he had a gun, threatening to shoot a member of his family.
"The police got there about five o' clock in the morning and sealed the site off. Apart from having the steading blocked off, we were not affected too much and the road block was lifted about 1pm.
"Some people just saw the road cordoned off, so the rumour got up that there was foot-and-mouth or bluetongue on the farm."
His brother Robin, at Cutcloy, neighbouring the site, was also bemused by the goings-on.
He said: "The first I knew about it was when I saw a police car at my road-end with two officers sitting inside having their breakfast. They just told me they were dealing with an incident, but didn't go into detail.
"Then a neighbour contacted me to say there were police with dogs at the top of my hill. Being nosy, I went to have a look, assuming they must be looking for drugs.
"It was only later on I heard what had really happened. They say this man has a drink problem and had got drunk then phoned the police to say he was armed.
"I did hear of one poor guy who came out of his caravan with a cup of coffee in his hand to be met by armed police telling him not to move in case he was shot at.
"That would certainly make the coffee taste a bit funny."
One local, who didn't want to be named, said that the family in question were regular visitors to the holiday park.
Sergeant Tom Findlay, a tactical specialist, was involved in the uncompromising police operation.
He said: "At the outset of the incident our primary concern was the safety of the public, the staff, the subject involved and our officers.
"In response to the call, we deployed specialist firearms officers and trained negotiators. A male person was subsequently taken into custody."
But the sergeant confirmed that it was rare to have that level of response to an incident in Dumfries and Galloway.
He added: "There are strict guidelines when specialist units are used. There has to be a potentially serious situation before we deploy firearms officers."
Police confirmed yesterday they are still investigating the incident.
A spokesman said: "As a result of the incident, a 33-year-old man from the Girvan area was apprehended.
"Inquires are currently ongoing at this stage in relation to the incident and a report will be prepared for the Procurator Fiscal."
No one at Burrowhead Holiday Village was prepared to comment.