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Mr Rivers (65) was the owner and skipper of a jet-boat that first got into trouble while negotiating the Wilkin River, which flows into the Makarora River.
His body was recovered by police yesterday morning near the mouth of the Makarora River, at the head of Lake Wanaka.
Tim Rivers said yesterday his father had been "tragically taken".
"Murray was well-known in the community for his generous spirit and love of life.
"The family are shocked and deeply saddened by Murray's passing but thankful that his body was recovered so quickly."
Frustrated Queenstown harbourmaster Marty Black yesterday said his message to boaties was "wear the damn life jacket".
"A flooded river, in a boat like that; it's just common sense to wear bloody jackets," Mr Black told the Otago Daily Times.
Mr Rivers and a man and woman, both aged 23, had been jet-boating on the Wilkin River on Sunday afternoon when the boat's engine cut out.
Wanaka police search and rescue co-ordinator Sergeant Aaron Nicholson said yesterday the group began pushing and paddling the boat back to the ramp at Wharf Creek at the top of Lake Wanaka.
By the time they reached the bank, Mr Rivers and his boat could not be seen. The two, one from Invercargill and one from the Wanaka area, walked through farmland to the Makarora village and raised the alarm.
Search and rescue teams, the Hawea marine group, Wanaka coastguard and a helicopter with night-vision equipment were called in about 8.30pm on Sunday.
The 5m aluminium jet-boat was found early in the search, beached on a shallow section of river braid near the mouth of the Makarora River. Although the search continued until 3am, there was no sign of Mr Rivers.
His body was found when the search resumed yesterday morning, snagged below the surface by a submerged willow tree about 150m from the jet-boat.
Sgt Nicholson said it appeared life jackets "were not worn by any of the jet-boat occupants".
One week ago, the ODT reported a Papakaio couple's message for whitebaiters "and anyone else in the water" to wear a life jacket after 21-year-old Victor Boraman was swept out to sea at the Rakaia River mouth.
Ted Boraman said he believed his son would have survived if he had been wearing a life jacket.
The Otago Regional Council website shows 102mm of rain fell in the Makarora area in the week to yesterday, and water levels in the area rose sharply on Saturday.
Mr Rivers was a partner in and manager of Alpine Fencing Wanaka Ltd, specialising in macrocarpa post-and-rail fencing.
A business partner, Marc Simmonds, said yesterday the firm would continue to operate.