H. T. Burleigh was black, the grandson of a slave.

This is the dialect Burleigh knew from his youth, and his rendering of it. Not some white's interpretation.

Burleigh was well-known as a singer and composer, studying under Dvorak. His setting of "Deep River" had much to do with establishing the spiritual as an art song form and making them familiar to a new audience. He never forgot the plantation melodies of his childhood. See the following brief biography:
Burleigh

It must be added that "Songs of Zion," the book from which this spiritual was taken, originated from the leaders of Black churches. "Growing out of the Consultation on the Black Church in Atlanta, Georgia, in 1973, sponsored by the Board of Discipleship, was a specific recommendation that the Section on Worship develop a songbook from the Black religious tradition to be made available to United Methodist churches." The Black editors, Nix and Cleveland, made a great contribution to African-American sacred music .