That's the bangkok post graphic that mis labeled the requirement that the flight must be chartered. Also, this is the 1st I've seen stating Thais don't need health insurance. As of now, Thai nationals need to buy covid coverage if their domestic plan won't provide the certificate (most haven't been). I wouldn't take this info graphic as law.
I know Phuket if you're not vaccinated you need a negative covid test to enter, not sure about the other islands. Chiang Mai if you fly in they do the free swab at the airport that comes back in 5 minutes.
Covid insurance to enter the country and Non-OA insurance are 2 totally different things. For covid insurance it can be from anywhere, but the insurance company needs to be able to issue a certificate specifically stating your covered in THailand for covid up to 100k usd.