This doesn't really seem like a change. And I find it hard to believe that the goal is to find overstays, since the documents will be checked by the usual teenage contractors, not immigration (and you can still use ID other than a passport).
That's just very strange - I wasn't aware that the US would be checking the reentry qualifications of someone DEPARTING the US. Did they show you the message that they said came from US authorities?
The OP has explained that she's still in the US and was trying to board the first leg of a round-trip journey to Thailand (I had also assumed she was in Bangkok and trying to return to the US).
The green card itself should be all that is needed to enter the US as long as the holder has been abroad less than one year. If she has been out more than a year, she should have applied for a reentry permit before departing the United States. You can Google "US reentry permit" for more info.
Sorry, I didn't express myself clearly - I was just noting that the situation you described was an out-and-out scam, while the one mentioned in the OP was just a case of accepting a bad exchange rate.