Has her fridge been playing up lately (which it had

He got a hit, had the answer been no, he would have moved on to something else.

Had she been experiencing the lights flickering in the house (which she had)

A common experience and again a hit.

He said that it were her Nan.

He could have said it was anybody who was unlikely to be alive.

He asked her if she knew anyone older whose name began with a B.  She answered no,

No hit so he quickly moves on.

We sat there bewildered.

You had just had the oracle performed on you by a quick talker.