The others were found on the beach of Motuketekete Island just before 10am on Wednesday.
They were in the icy water for about three hours and had to swim 2km to get ashore. It is suspected the men were drinking on the boat, and possibly before they went out on the water.
"That is one of the aspects that's being looked at, to see if it was a factor in the accident. It is definitely something we are talking to them about," he said. "But that's all I can say about that at this stage. It is a matter for the investigation down the stream."
Two of the men remained in North Shore Hospital last night.
The men were due to be discharged on Thursday, but their conditions were more serious than doctors originally thought.
"There is an obvious concern for their health, but generally they're fine. It's just the risk of something developing, which is why they're being kept longer than expected," said hospital spokesman Errol Kiong.
The father and son have been discharged.
Mr Paget said a decision would be made on Monday as to how long the search for Mr Preston, who has a young son, would continue.
"We will slowly scale it back over the next couple of days. On Monday I'll review and see how much we do or don't do - with a view to perhaps even changing our focus to see if we can spend time recovering the boat.
"If Mr Preston isn't found by Monday, chances are we'll have to wait for nature, which will hopefully bring him to our attention."
Mr Paget said an underwater camera was not an option.
"We don't have a clear enough defined area to search under water. We're using other equipment to see if we can narrow that down a little bit. But it's a slow process."
There had been no sign of the boat, and nothing had surfaced from the wreck since the first day searchers were on the water.
