Because the subject of the sentence is 'one percent', which is a singular noun - hence the 3rd person singular verb, 'owns' . That said, I think the sentence reads awkwardly with a singular subject. It would sound more natural to treat 'one percent of people' as a plural subject - referring to several million people - and say 'own'.

You are talking about them ( The people - They) so the verb is 'own' I - own You - Own He/She/It - Owns We - Own You - Own They - Own