As others have pointed out, Timatic is a source considered authoritative by airlines. Timatic says you don't need 6 months on your passport and I would cite this information in your letter to the airline. The online Timatic database is provided by Delta Airlines for free here.

The problem with the quote from MFA provided above is that I saw the same information provided by the Thai Embassy's website and it is obviously out of date. It says that visa-exempt tourists can only spend 90 days in any 6-month period in Thailand but that is an old rule that has been done away with by the country's immigration authorities. As weird as it is to say, the Thai Embassy's own website cannot be treated as an authoritative source. To unravel the truth, one would have to consult a lawyer who can read Thai or an official at Thailand's immigration bureau. Primary sources are the only thing that really matters -- second-hand sources in English don't matter.

The fact that there is so much misleading and conflicting information out there probably works in your favor. You should have been offered the opportunity to sign a waiver. The notion that the airline made its decision based on something they heard from Thai Airways is also unacceptable: airline employees are not immigration lawyers and should not be treated as such.

Update: The Thai Immigration Bureau website also makes no mention of any passport validity rule for visa-exempt tourists. Check it out at www.immigration.go.th.