At first blush, I imagined that the passenger had removed all the clothes of other passengers--and then proceeded toward a flight attendant. (In the circumstances, perhaps not all that inappropriate. It has been very hot here in America.)

As I see it, in the Daily Mail sentence ("The unidentified passenger took their clothes off ...") there is only one possible antecedent for their, i.e.: "the unidentified passenger", so it has to be interpreted as a singular they, but in the Washington Post sentence ("Officials say a Spirit Airlines flight leaving Las Vegas was briefly delayed after a passenger removed all their clothes ...") there are two possible antecedents: "a passenger" and "officials". The second (obviously unintended and therefore funny) interpretation also permits "all their" to be interpreted as "of them all".

 

I briefly wondered if the Daily Mail's " ...  was removed by police and required medical attention afterwards" was intended to suggest the possibility of police brutality (post hoc ergo propter hoc), rather than a medical condition but I quickly realized that the Daily Mail wouldn't do a thing like that.