Nothing in that sentence is in potential form. That section of the grammar guide is basically explaining 見える and 聞こえる because they often get lumped in with potential form even though they are not potential form.
I think your confusion is coming from the fact that て-form can sometimes be used to indicate a reason, explained here: te-form (て-form) for Cause or Reason - Learn Japanese Online
So another translation of the sentence could be “Because it cleared up today, Mount Fuji is visible”.