From what I learned in my microbiology class... the genes which confer resistance to antibiotics are present in bacterial populations, but not necessarily every individual bacterium. Additionally, through a process that is sort of like the bacterial version of sex, called Horizontal Gene Tranfer, one microbe can transfer the genes which confer resistance to antibiotics to another bacterium on plasmids, which are basically small circular rings of DNA.
So basically, it takes energy and resources to turn that gene into the proteins which will deactivate the specific antibiotic, so if the bacteria is never coming into contact with the antibiotics, there's not really a reason to keep that gene around. But if suddenly a bacteria population were to find itself in a hospital environment, where surfaces are being disinfected very frequently, not only is it extremely beneficial to keep the antibiotic resistance genes around, but also they are being actively selected for, since all bacteria without those genes are being killed off.
Horizontal Gene Transfer can happen between bacteria that are not even the same species. So for example, the Hero Bug that this article is talking about, if it were present in the hospital environment, might be able to send over a methicillin-resistance plasmid to a possibly pathogenic bacteria like Staph, and create MRSA. But if the pressure to remain resistant to methicillin was removed from the staph populations, by no longer using that antibiotic to treat the infection for several years, the staph cells would eventually mostly "forget" how to resist that antibiotic by no longer ensuring that the resistance gene is included in every bacteria in the subsequent generations. Probably about .01% of the bacterial cells would keep the gene even if it was not required for their survival, and once we start using the antibiotic again a few years later, wiping out most of the bacteria is usually good enough to help the immune system take care of the ones that are left.
This idea of holding off on using a specific antibiotic for a while is called antibiotic rotation. Here's a paper where they tested the efficiency of the idea: https://www.ncbi.nlm.nih.gov/pubmed/17693828
Here's the wikipedia article on horizontal gene transfer: https://en.wikipedia.org/wiki/Horizontal_gene_transfer
Plasmids: https://en.wikipedia.org/wiki/Plasmid
And antibiotic resistance: https://en.wikipedia.org/wiki/Antimicrobial_resistance
tl;dr: The overuse of antibiotics can lead to bacterial populations developing resistance to those drugs, but since the chemicals in "natural antibiotics" have been around for a long time before we started using them, the genes to counteract them already exist, but are not always expressed.