From the same paper:

"Higher marginal tax rates are associated with increases in gross wages and earnings."

The part that you cited is where they cite the old papers by other authors. They also say why conclusions of those papers might have been wrong:

"Moreover, we show that ignoring the potential labour supply response to a tax change, following the methodology of Gruber (1997) or Anderson and Meyer (1998), as well as ignoring the endogeneity of the marginal tax rate, may lead to the erroneous conclusion that the tax is fully incident on equilibrium earnings."