The appeals process is spelled out in Rule 10.01(a) and is one of the longer rules on the books:
The official scorer shall make all decisions concerning judgment calls within 24 hours after a game concludes or is suspended. A player or club may request that the League President review a judgment call of an official scorer made in a game in which such player or club participated, by notifying the League President in writing or by approved electronic means within 24 hours of the conclusion or suspension of such game, or within 24 hours of the official scorer’s call, in the event the official scorer changes a call within 24 hours after a game concludes or is suspended, as provided in this Rule 10.01(a). The party requesting review shall submit, before the close of the second business day of the league office following the request for review, any written explanation or other evidence (such as videotapes or electronic media) the player or club wishes the League President to consider in reviewing such request. The League President shall not consider any evidence submitted after the time for submission set forth in this Rule 10.01(a). The League President, after considering the evidence submitted and any other evidence he wishes to consider, may request that the official scorer change a judgment call or, if the League President concludes that the judgment of the official scorer had been clearly erroneous, may order a change in a judgment call. No judgment decision shall be changed thereafter. A league may impose a reasonable fee upon a party requesting such review in the event that the judgment call of the official scorer being reviewed is upheld.
Pittsburgh official scorer Bob Webb can only be strongly suggested to change his call by the Commissioner's Office. The rule leads me to believe that the Commissioner's Office (written as "League President" here) would only unilaterally make a change if Webb had made a call clearly in error (such as awarding the wrong player a putout on some odd play.)
It is possible that we won't know if the Brewers request for a writ of certiorari will be granted until tomorrow.