A second possibility was that "maybe some villagers are not happy with the protest ... and the guards have been harassing people for money, and harassing women," the police chief said.
He denied rumors circulating among some of the protesters that authorities staged the attack in an effort to scare away the protesters.
Hundreds of rubber farmers have taken part in the protest in the Cha-uat district of Nakhon Si Thammarat, 580 kilometers (360 miles) south of Bangkok.
The farmers are calling for the government to guarantee the price of rubber to help increase their incomes. Rubber prices in Thailand have continually dropped since peaking in 2011 due to weaker demand in a sluggish global economy.
In negotiations in Bangkok last week, representatives of the farmers demanded the government fix a price of 120 baht ($3.70) per kilogram for rubber products, but the agriculture ministry made an offer of 80 baht ($2.50) per kilogram.
Thailand is the world's top producer and exporter of natural rubber, which is used in products from condoms to car tires. The government already subsidizes rice growers by paying them above-market prices, a scheme that has accumulated losses of at least $4 billion since its inception two years ago and resulted in Thailand losing its spot as world's No. 1 rice exporter.
The demonstrators have said groups of rubber farmers from other parts of the country will stage separate rallies on Monday.
At the site of Sunday's shooting, angry protesters blamed the government.
A protest representative, Iad Seng-iad, said that if the government had accepted the farmers' demands, the protest would have already ended and nobody would have died Sunday.
"The government must take sole responsibility," he said in a statement read to reporters in Cha-uat district. "Our brother who died was neither a thief nor a convict. He was a farmer in trouble."