My sister said this last year... when she was 18! I don't know if this counts but she believed it when she said it and didn't get why I was laughing at her until I explained it to her very slowly.
Apparently she's always been under the impression that since she's one year older than me, she has known me for one year longer than I've known her.
A childhood belief about getting older

others believed things like this
- Abba - Happy New Year
"Kangaroo year,
Kangaroo year..."— Santa Puncher - i used to think that if i didn't celebrate my birthday each year my younger sister would catch up with me— q
- i thought I got one year older when my family sang the birthday song.— I am the ghost
- My sister thought (not more than one year ago, she is now 14) that John Doe was an actual person.— Brother to Natascha
- My sister uesd to think that you did a whole year's worth of growing in the night before your birthday.— Richard Davies
- I thought that 1983 went on for 3 years - had to ask my sister who decided how long a year lasted.— Sally