The rational was: Bacteria becoming resistant due to a treatment has only ever been proven for a handful of conditions( TB , HIV syphilis, and so on). The other bacteria are ether resistant or they aren't prolonging the treatment does not encourage a resistant mutation.
By prolonging your treatment with antibiotics you create an environment in which antibiotic resistant bacteria, both the good and bad kind, can replicate easier. Due to Horizontal gene transfer good bacteria can transfer their antibiotic resistance to bad bacteria.
This advice is in stark contradiction to the Fleming quote.
I heard it on the radio and can't remember the sources, but it makes sense to my non medical mind.
*edit added sources.
Found the journal entry if anyone cares : https://www.bmj.com/content/358/bmj.j3418
Article about journal entry : https://edition.cnn.com/2017/07/27/health/antibiotics-course...