Some policies will cover you overseas, but even if they do, you will have to pay up front in Thailand, and then apply for reimbursement from the insurance company.
If most of your income is from investments that's true, but if the majority is from Social Security or a government pension, the DTA excludes those from being taxed by Thailand, and considering that you get a credit for the total US taxes paid, many people would wind up not owing any Thai taxes.
If you're from the US, the DTA specifically excludes Social Security and any other governmental (i.e. state or local) pension from taxation by your country of residence. So if your main income is from Social Security and/or a governmental pension, and that's the money you're transferring to Thailand, conceivably you don't owe any taxes in Thailand.
For any US expats, the double-taxation agreement between the US and Thailand specifically says that Social Security, and any other Governmental pension (i.e. State or Local pension) can ONLY be taxed by the United States (see Article 20), therefore Thailand could only potentially tax you on any other income. (and again, under the double-taxation agreement, Thailand Must credit you for any taxes paid to the United States.
A difference without any meaning. Under a double taxation agreement, you can be "taxed" by your country of residence, BUT, you get a credit for any taxes you paid to your original/home country.