Since It Happened out of state and eight years ago Should I even state it in my records to a future employer?

If someone does a background check Will it show up? I am going to be going to work for a private music teaching company but there’s this hitch: They INSIST That no instructor They hire Can Have ever been arrested for any Cause whatsoever, innocent or guilty alike. I Realize They Are worried about drunk driving and child molestation, but if I with hold this information, They May Find Out. What do I do and what are my rights?