The GOP at the time had a theory of why: Jack Kemp, Dole's running mate. The joking version of it at the time was "Jack Kemp has showered with more black men than most Republican politicians have shaken hands with," but in all seriousness, as former Quarterback of the Buffalo Bills, Kemp pretty uniquely for a non-CBC politician came up in a professional environment where many of his colleagues and peers were black and how to have serious professional relationships with them, and that was basically his selling point in Republican politics.
Whether or not Kemp ACTUALLY had any special black appeal is a very difficult question, but the GOP certainly THOUGHT he did.
This.
Kemp could have won 10%-15% of the black vote against a dud like Gephardt or someone else.
I mean, Dole allegedly won 12% of the black vote in 1996 with Kemp on the bottom of the ticket, if you trust exit polls. Personally, I see no way that Clinton could've won the black vote only 84-12 (technically, 1992's 82-11 was worse on margin and so Clinton twice got the lowest black margin since 1976 when Carter won the black vote 85-15...but this can't be true...can it?) and won by 8.5% nationally, but that's the data we have. Kemp's as good a rationale as any.