I've seen that posted as well. The A.S. Booth buried in Riverview Cemetery, is I believe, Frederick's son, Alonzo S. Booth. He was born 8 Jan 1848 d. 24 Feb 1907. This would make he 59y, 1m, 17d.
On the Shenandoah website there is a cemetery listing by cemetery and by alphabetical listing. The listing by cemetery provides a picture of the AS Booth stone. The stone states born with a difficult to read date, but the year is 1848. I think what happened was whoever made the alphabetical listing took the birth date and used that as the death date with the provided age. That would give you the Nov 1788 birth date.