@David *******
yes, same applies for the UK on military, Police, Fire Government Pensions. I have a UK Government Pension. The DTA states its taxed in the UK only and Thailand has no claim to it. However, for example my UK rental income is always taxable in the UK but that doesn't mean that Thailand cannot also tax part of it if I bring it into Thailand. The DTA just prevents the same money being taxed twice. Any tax I've paid in the UK on this rental income, I could claim a tax credit for, so that money is not taxed twice. But any difference would be taxed in Thailand.
Expat Tax Thailand has a great website with loads of useful info and recorded webinars.