My thoughts about mediums (genuine, not showbiz) is that some people do have a telepathic ability, reinforced perhaps by practice and by unconscience reading of non-verbal clues and an instinctive feeling for the personalty of others.
We all have inside us an image of those we love, we know how they would react in different circumstances, we are familiar with the lives they led, since and before we met them. If a medium can sense that picture, they can reproduce (innocently or intentionally) the personality that we remember, and can answer questions in character.
Where I am a definite sceptic, it is when exotic spirit guides are supposed to be contacting departed loved ones on behalf of the medium. What is that all about? Why should an Egytian princess, say, waste her time taking messages from Auntie Gladys to Cousin Jean about looking after the canary?
And why do so many reincarnated people believe that they used to be Napoleon. Surely even if it were possible, they could only become one person at any given time? Unless they had split personalities and could time-share in different bodies?