ESTA for a US-born UK Citizen

So we're flying tomorrow from the UK to the US and my wife just discovered her US passport is expired!!

She's been married to me, a born-here UK citizen, long enough to have her own UK Citizenship and passport (that is current!)

Renewing a US passport takes weeks, and we tried applying to the ESTA scheme on her UK passport, but the initial response is "Travel Not Authorized".

Is that likely because they know she is a US citizen/passport holder and it's expired? Will it not work anyway to treat her as a UK citizen and she might need to do something else?