The rule about “bumping up” the comma to a semicolon in a compound sentence with a coordinate conjunction has to do with obscuring the division in the sentence. Does the other punctuation “hide” the break between the two sentences? Is there other punctuation that makes it difficult to see where the first sentence ends and the second one starts? One comma alone does not do that. It takes at least two, and then they have to be close the the comma before the conjunction.
…I met with John, my boss, on Friday, July 12; and we went over the reports.
…She said that, when he left, he took it all with him; but his brother, his sister, and I refute that.