@Paul ******
no where in domestic law or international treatiee does it state income is exempt of you already paid tax on it.
Generally, DTA make government pension taxable only from the government that issued it. Private pension are going to be taxable where you are a tax resident, which for retirees in Thailand, mean Thailand. It could even be taxable in both (then credited) depending on the souce country (US especially).
It also has nothing to do with your passport or citizenship, only the countries involved. If a UK citizen is receiving a pension from France and lives in Thailand, the factor of UK citizenship does not effect that.