understood. Still wrong, but anyway. By far would not be the first person to parrot wrong information. I would be compelled to in the least, contact that airline, express your grievance identifying it was wrongful and to compensate you. Just my opinion. š
Unless you omitted details this simply isn't true, is easily found on the US immigration site (as referenced already). So I'm not entirely certain why a google at the counter couldn't yield this information for you, took me 90 seconds to confirm. The counter worker for an airline has no business or benefit doing this when they're clearly wrong and a higher level of authority needed to be included.
Fwiw, when I originally applied for a visa I entered my name First Last and it was rejected because on my passport is First Middle Last though nothing on the application stated āas it appears in your passportā. I had to pay and apply again.
My point, donāt leave any room for something to go wrong, you could very well be sent back at the border. š