Are the claims about Jomtien Immigration changes and extension rules accurate?

If he's already at 66 days, he's 6 days overstay already. As soon as he attempts to leave the country anywhere he will incur a 500 baht per day fine, plus get an "overstay" stamp in his passport

Total BS

To answer the first question that is BS

Second question is true

It's half BS.

No office would just "stop" giving a standard extension, which the 30 day extension on visa exempt is. That's one of the simplest extensions to get in all of Thailand, and I'm not sure why you would ever go to an agent for that. You're just asking for trouble, because now you have a sketchy stamp from an office nowhere near you.

Jomtien is known as one of the most difficult offices in Thailand as they often send people away after they've waited in line, only to tell them to come back when they have 2-3 days left on their current stamp. But they are also known, or were known, as an office that issues a lot of bribery based extensions as well. This meant other offices didn't want anything to do with a passport that already had a stamp from Jomtien.

So you could have easily gotten a 30 day extension from Jomtien, but your agent's connections are not in that office, they are in Korat, so that's where they get their extensions from.

Visa exempt can get ONE 30 day extension. There are no other options after that. You would need to leave the country and enter again to get additional time in the country.