Thai Visa Centre is the owner of the group you are currently asking your question from. You can see their name on the banner above. Yes, they are legit. If it's "Center" with the wrong spelling, then probably a scam.
Or even better, let her call immigration and ask. The paperwork needed for marriage extension is quite extensive (way more then just a marriage certificate), but you are in a different situation then most of us. I'm on under-consideration stamp atm, so the process is very fresh. You can't mess up a single requirement or you get denied.
Let your wife call the district office and ask. Most people like me who are married to Thai wife got married in Thailand, your situation is a bit unique.
"More likely the agent does a monthly trip to immigration". Incorrect, most agents do not go to immigration at all, unless they are in Pattaya or Chiang Mai. In every other province, agents are not the one processing your passport, people way above them do.