The data in DIGITRAD has a problem. Although there was another accident in 1959 that killed nine workers closer to the surface, this accident did not occur in 1963, it occurred in May 1965 -- and this song was written by Kay Cothran and copyrighted in September of 1965. She said in the copyright that the tune was an extensive reworking of Streets of Laredo. The information eventually was published in a government report, but the papers were quite quiet about it at the time, hence the outrage that sparked the song.

Source for the disaster details: https://usminedisasters.miningquiz.com/saxsewell/C_L_Cline_No2.htm

C. L. Kline Coal Company
No. 2-A Mine Explosion
Robbins, Scott County, Tennessee
May 24, 1965
No. Killed - 5
USBM Final Investigation Report (2.3 Mb)   
An explosion, originating in the face area of the left main aircourse, killed all five men in the mine. The explosion occurred when a methane accumulation was ignited by a cigarette lighter. The methane was emitted from crevices in the roof near the face.

The mine was classified non-gassy by the State. The owner-operator was the only one that possessed a flame safety lamp. He reportedly made a gas check during his pre-shift examination.

Ventilation was inadequate. The mine fan was not capable of supplying air flow appropriate to the size of the mine. Also the eight inby stoppings in the mains were constructed of brattice cloth and the left main aircourse was advanced 300 feet inby the last open crosscut with a line curtain terminated 25 feet from the face.

Dust from coal on the conveyors and from spillage along the conveyor lines entered into the propagation.

Source:
Historical Summary of Mine Disasters in the United States - Volume II