This guy is 78 born in 1930, so if his father was say 20 when he was born his father was born in 1910 and his grandfather if the father was 20 at birth of grand father was 1890, slavery was well over for 40 years.
Add 10 years all around still doesn't work.
Unless his grandfather was a slave in Africa where black on black slavery was practiced well into the last century (and probably still exists today).
The father died in 1935. If, in the article, they gave his age at time of death, I missed it. The former slave grandfather died before the now 78-year-old grandson's birth in 1930. Again, no details are given as to grandfather's date of death and age at the time of death.
In any case, the Emancipation Proclamation was signed in 1862. If the grandfather was a child at the time, and if he was in his late 30's or early 40's when his son (who became the father of the subject man in this article) was born, then the timeline would work.
Say the slave grandfather was 5 in 1862. He would have turned 40 in 1897. If his son was born that year, he would have been 33 when the grandson (now 78) was born in 1930.
So it is possible that this man was the grandson of man who was born into slavery. The grandfather could even have been 10 or 12 years old in 1862, and the timeline would still work. However, the grandfather would have lived the majority of his life as a free man.