Well techically it should qualify on land borders, but because of corrupt land borders and corrupt IO's people that qualify for 90 day visa exempts are being hassled for tea money it seems. So in that context maybe flying out and in is advisable.
Yep, the OP is asking: If he goes out via a land border such as Myanmar and comes back does he get 90 days. I understand visa exempt permissions of stay derived from bilateral agreements are not extendable at local Immigration, so he gets 7 days to leave, but he was asking something else there.
I think what you are referring to, Robert Lagas, is that some visa run agencies are saying South Korean nationals cannot do same day in-outs at land borders. However, upon entering Thailand, regardless whether it's by air or land border, South Korean nationals are entitled to a permission of stay of 90 days. And this is confirmed by many websites. Otherwise South Koreans would not be allowed to enter by land visa exempt, which is ridiculous.
Take a flight to Vientiane. That's the best advice I can give you. You are not going to navigate through this bureaucracy, even the hurdles you had to go through so far I find ridiculous. It will cost you more, stress you more and with an unlikely positive outcome.
Cut your losses and fly out to a friendly Consulate.
The first booth that says re-entry permit is actually a "disguised" application form and photo taking service. You give her 1,200 baht, she takes your pic, prints the form, gives you back 1,000 baht and a receipt for the 200 baht service fee, and sends you to the back office located 10 meters away. It's misleading but better than before.
You can skip that booth and go to the back office if you bring your application completed from home with your own pic. I learned from own experience by being done for the extra 200 baht, an Indian group of 8 before me had them all done from home.
I think some here are taking this anti foreigner media propaganda too seriously. It would not be the first time I have seen made up numbers in Thailand.