In August 1968, an outbreak of infections of a particular strain of streptococci — Streptococcus pyogenes to be exact — occurred at Vanderbilt University Hospital in Nashville, Tennessee. The nine patients infected were housed in different wards with different problems, and they were visited by many medical staff during their stays.
But seven of them shared an anesthesiologist. (Cue that cool police procedural show music again.) The staff took oral swabs of the anesthesiologist's skin and throat, but they came back negative. No trace of the streptococci. Since this was the mid-20th century, when penicillin was handed out like candy, the anesthesiologist was given a short course of the antibiotic. Because why not?
But a few months later in November and December, another outbreak of the same strain of strep infected eight different patients. The same anesthesiologist attended five of these new cases. He still wasn't showing any symptoms, but this time the staff took an anal swab of the doctor and that turned up the exact strain of strep effecting these new patients. The anesthesiologist was given a full round of antibiotics and taken off duty for 10 days. Afterward, his cultures were clear of streptococci and there were no further wound infections related to his patients.
Researchers at the time said in The New England Journal of Medicine that while the "anus-to-hand-to-patient rout of transmission" was a possibility, airborne transmission was more likely in this case. The authors of the NEJM paper concluded, then, that it was probably the doctor's farts infecting the patients' wounds, not him washing his hands improperly.