Do we need to believe in Buddhist stories to be a real Buddhist?

Some suttas and the dhammapada contain stories with things not very easy to verify, such as people flying, living 8.000 years, teletransportation, etc. Some of those are related to the psychic powers of the Buddha and that is easier to believe as he was an enlightened being; however some are not related to that. Buddha always encouraged us to verify and contemplate things. Will having doubt about Buddhist stories and legends interfere with Buddhist practice?