UPDATE: See below

Jonathan Head of the BBC has another update. Key excerpt:

Like the hundreds of other asylum-seekers from this Burmese Muslim minority who have arrived on Thailand’s Andaman Sea coast, they have been handed over to the Internal Security Operations Command (ISOC), a military authority set up under the Cold War and still given sweeping powers to protect national security.
The local commander of ISOC in Ranong, Col Manas Khongpan, has denied these allegations. He told the BBC that illegal immigrants are never held by his troops.
But that contradicts comments the BBC has been given by other military and police officials, who say all Rohingya boat-people are now being handled by ISOC.
Some of those officials, who did not want to be named, confirmed that Rohingyas had indeed been set adrift at sea, with little food and water.
The Thai government has now issued a statement saying it is investigating all the facts surrounding these allegations.
It has promised to re-assess the situation of all illegal immigrants in Thailand, numbering perhaps three or four million, most of them from Burma, and to treat them in accordance with humanitarian principles.
Whether it can truly hold the military to account though is open to doubt. In many areas of Thailand the army operates with little civilian oversight. It has huge secret budgets, and extensive business interests.
The current Democrat-led coalition was stitched together last month thanks to the intervention of the powerful army commander General Anupong Paochinda – he may well resist any calls for his men to be brought to justice over these allegations, as his predecessors have.
But it is also worth remembering that under the most recent constitution the most senior commander of ISOC is, in fact, the Prime Minister Abhisit Vejjajiva.
He has made the rule of law one of the core principles of his administration. Any crimes committed by ISOC personnel, whether against Thais or illegal migrants, will ultimately lie at his door.
BP: ISOC was strengthened and given more powers by the Surayud government after the military coup – actually it is the Internal Security Act (Section 5) and not the Constitution which makes the PM the Director of ISOC.
Oddly, the Thai denials seem to have focused on how the military treated the Rohingyas on the beach and that they were no mistreated – see some new pictures of them being held on the beach here. This seems to miss the point as the central criticism of the Thai military has not been on how they treated the Rohingyas at the beach based on the photos (it is still an issue), but on the allegations that they throw four people overboard with their hands tied up, and then leaving the Rohingyas in the middle of the sea after removing their engine and only giving them enough food for two days, and thus causing the death of the Rohingyas. 
Former British PM Macmillian was asked what was the greatest obstacle to political achievement and he replied ‘Events, dear boy, events’. This is more a problem for Abhisit with the international community, foreign journalists, and members of the NGO community (well one assumes they disapprove as so far have heard little comment from them) for now than with the Thai public who are more concerned with economic considerations. However, as Jonathan notes Abhisit have made the rule of law one of the core principles so he can’t ignore the issue and it will be a test of whether he is all style and no substance. You also have Foreign Minister Kasit saying a few weeks ago:
Kasit also asserted that Thailand will observe human rights and environmental concerns. ”We shall treat the Burmese as we do Thais. We will not do anything to jeopardise the Burmese community.” 
BP: Kasit has been rather quiet, but one wonders how long this will last.
There is also a question of Thai-Indian relations given some recent statements in India as AFP reports:
India’s coast guard said Sunday it had rescued hundreds of the refugees from the Rohingya ethnic group, who live along the border of Myanmar and Bangladesh, but that hundreds more were feared lost.
They said they were taken to an island off the Thai coast and beaten up before being forced into boats and pushed into the high seas,” said Ranjit Narayan, a police official on India’s remote Andaman and Nicobar islands.
“We fear several hundred are still missing,” coast guard commander S.P. Sharma told AFP. He said India had rescued 446 refugees from four boats since the end of December.
Those figures are in line with those of the Sunday Morning Post, a Hong Kong newspaper, which said it had compiled a toll of 538 missing or dead.
Sharma said the migrants said they had been arrested by Thai officials and set adrift without engines or navigational equipment.
“Some survivors also said their boat was towed out to sea by the Thai navy and given two sacks of boiled rice and two gallons of water before being abandoned in the middle of the sea,” he said.
btw, PRD have articles on what Abhisit and Anupong have been saying on the issue.
UPDATE: A reader notes in the comments this AP story from December 31:
Indian officials battled strong winds Wednesday to retrieve the bodies of at least 10 suspected illegal immigrants that washed ashore on the remote Andaman islands, as a search continued for 300 others missing and feared dead after reportedly jumping from their disabled boat.
Coast guard officials discovered the bodies Tuesday but were unable to reach them in a mangrove swamp that is inaccessible by land. Heavy waves and wind hampered an approach by sea, said S.P. Sharma, the coast guard inspector-general on the Indian-ruled islands.
The coast guard rescued 105 people on Saturday from the rickety wooden boat found drifting off the coast. Two more survivors were found Monday but none since, Sharma said by telephone.
Survivors told Indian authorities that more than 300 people from Bangladesh and Myanmar had jumped from the boat, which had been drifting for 13 days, and tried to swim to shore.
Sharma said they had no independent confirmation of the number of people aboard the boat, but the condition of the rescued survivors was grim.
The overloaded boat, about 65 to 80 feet (20 to 25 meters) long, had no covering to protect passengers from the harsh sun and had inadequate food and water, he said.
They were dehydrated and some were unconscious,” Sharma said. “They were in a state of shock and trauma, both mental and physical.”
The boat’s mast was gone and it had no engine, he said.
The boat’s passengers were apparently heading for Malaysia by way of Thailand, where they were supposed to pick up a guide for the second leg of the journey, Sharma said.
The survivors said they had been detained by Thai authorities for illegally entering Thai waters and then were sent back out to sea. Thai officials have denied turning them back.