That’s not exactly true. FMT isn’t going to fix your MRSA colonization, and it doesn’t inherently remove resistance genes from the population of bacteria in your gut. If those genes produce a survival disadvantage, they may be selected against and become a minor serotype in your GI tract, but that doesn’t mean that it is eradicated.
Also, you seem to be sharing a lot of links from humanmicrobiome.info, which I would advise against. While I can appreciate the primary author’s dedication to the topic and willingness to cite his sources, his website is not peer reviewed, and he explicitly states he is a proponent of FMT, introducing bias which is not being balanced by a peer review process. Not to mention he admits he is a layperson with no formal medical training/experience. I would direct you to IDSociety.org which is the home of the Infectious Disease Society of America, who publishes the actual guidelines used by infectious disease physicians in North America.