This is patently false. Until the late 1950's the out of wedlock black birth rate was under 20%.
If the legacy of slavery is a root cause of out of wedlock babies then logically the percentage should have been higher the closer we get to 1865. But the reverse is true. Slavery and Jim Crow laws had the affect of bringing black people together out of sheer survival and necessity. This placed a great importance and value on the black family. Black people were not allowed to be part of the greater American culture/society so they created their own. They created their own universities, their own towns, their own businesses, their own sports leagues. There were men like Frederick Douglass, W. E. B. Du Bois, Booker T. Washington, Paul Robeson, Jackie Robinson, any many more black people of prominence pushing for equal rights.
On a side note I'm currently reading Frederick Douglass' autobiography,
The Narrative of the Life of Frederick Douglass. Here is a black man who was born a slave yet through determination, intelligence, and great courage fought for his freedom and for the freedom of others. He taught himself how to read as a slave (it was illegal for whites to teach slaves to read). Douglass' Christian testimony is powerful and inspiring.