I agree with what's already been said, that there's crying and there's whinging and they're not the same thing. When Aurelia was a young baby she had horrendous colic and all hours of the day and night. For a period of time, this was coupled with breast refusal and there was just nothing I could do to calm her. I did actually leave her in her basinette in the bedroom and took a few minutes to calm down, and she stopped crying. I felt terrible about it, at the time. I would also rock her to sleep in her pram (with the reversable handle turned so it faced me), which was the only thing that worked but also meant she spent a loooong time crying before eventually falling asleep. In these situations, she was sort of 'left to cry it out' but I still wouldn't call it controlled crying - mostly because I wasn't in control of her crying at all CC is really when you deliberately leave them for increasingly long periods of time so they 'learn to fall asleep on their own'.
FWIW I think you can teach a baby to fall asleep alone without doing CC - I used to calm DD down, put her to bed and leave the room, and come back in as soon as she started crying. It took a number of goes but for a while she was actually falling asleep by herself quite easily. Trouble is as soon as a new tooth started to pop through or she had a growth spurt, it all went out the window