Olivia Culpo had to throw on her BF Christian McCaffrey's hoodie before her flight to Cabo ... and it wasn't due to cold weather -- it's because the airline told the 2012 Miss Universe she was showing too much skin.
OC's sister, Aurora, documented the whole debacle on Thursday ... showing Olivia in an all black outfit with biker shorts, a crop top and long cardigan.
Aurora says OC was called up to the front desk at their gate before boarding ... and one of the American Airlines workers told her she needed a blouse in order to get on the flight.