Addendum to: Predictions for Higgs production at the Tevatron and the associated uncertainties

In a recent paper, we updated the theoretical predictions for the production cross sections of the Standard Model Higgs boson at the Tevatron and estimated the various uncertainties affecting these predictions. We found that there is a large theoretical uncertainty, of order 40%, on the cross section for the main production channel, gluon-gluon fusion into a Higgs boson. Since then, a note from the Higgs working groups of the CDF and D0 collaborations criticizing our modeling of the $gg\to H$ cross section has appeared. In this addendum, we answer to this criticism point by point and, in particular, perform an analysis of $\sigma(gg\to H)$ for a central value of the renormalization and factorization scales $\mu_0=\frac12 M_H$ for which higher order corrections beyond next-to-next-to-leading order (that we discarded in our previous analysis) are implicitly included. Our results show that the new Tevatron exclusion bound on the Higgs boson mass, $M_{H}!=!158$-175 GeV at the 95% confidence level, is still largely debatable.