Tips are based on a *percentage* of the bill. So, why would it matter how much money each of the groups make?
Because when money's tight, you're more likely to "grade" the service you received more strictly (since that saves you money on the tip you think they earned), whereas when you've got money to burn, you're more likely to be magnanimous and tip more extravagantly.
Your perception of how precious each dollar bill is at the moment varies with how many you've got to spare, and that affects your tipping generosity.
So the point is that the apparent "racial" difference in tipping size may not be racial/cultural, it may be economic (and thus further investigation may discover that the real split is poor vs affluent customers, regardless of race, it just looks like a "black" thing because blacks are, on average, less affluent).