Actually I found that having to modify the nvd3 source code was not a real solution there.
So I simply added an overriding CSS rule that hides any exactly 1-pixel-height rect out there.
Still not optimal, but we'll have to wait for a new version of nvd3 with hopefully a fully configurable model to do that properly.
.nvd3 rect[height="1"] {
display: none !important;
}