I don't know, I really don't feel like it is. I think it's pretty clear that the choice of "unhappiness"/"sadness" is to clearly put it in opposition to the popular "money doesn't bring happiness" cliche, not out of some absolute claim on the magnitude of the suffering the lack of money could bring (so, merely sadness, but not agony, desolation, suffering, or any other stronger negative emotion one could choose).

It just makes the propositional logic of the sentence clearer:

X might not imply Y, but !X implies !Y