You said something very similar a few days ago. Even if it is "just" a secondary infection and if it's not or was not causing the EC in the first place, it might very well prevent the cheilitis from healing. When you reread sebs post, he was diagnosed with Staphylococcus aureus superinfection, and superinfection is another term for "secondary infection". They often occur e.g. with atopic eczemas, aggravating the condition. Secondary does not (necessarily) mean that you can just ignore it and that it does not have anything to do with the condition
And you using antibacterial creams for a while might not have been enough. Again, looking at sebs posts, he is doing a LOT of things to prevent a reinfection with the bacteria, using surgical washing liquid stuff on many parts of his body, changing his pillow casing every day, even storing his towels etc separately from his wife, etc., etc. His doctors surely did not instructed him to do that for the fun of it :-)