In the medical context as given, the only meaning is fainted, lost consciousness. It is clearly a quote from the patients who are using a natural and colloquial informal term.
The term "pass out cold" extends the colloquialism to indicate complete loss of consciousness.
Out for the count = boxers are counted out by the referee when knocked out in the ring.
Out like a light = a colloquialism saying a person went to sleep very quickly - one minute they are awake, the next they are asleep. All very young animals do this.