Action taken by the treasurer in accordance with the provisions of this section shall constitute diligent inquiry and the exercise of due diligence in an effort to collect the taxes with respect to which the action was taken as required by section 55 and 56a and elsewhere in the Michigan general property tax act, being Act No. 206 of the Public Acts of 1893. The treasurer or his bondsman shall not be liable for any taxes which remain uncollected because the treasurer, in his estimate made in good faith, has underestimated the taxes to be paid on any property with respect to which such action is taken.