The guy is talking about power cleans, not full cleans. Front squats are not going to help much beyond a certain point, and chances are you're beyond that point. And there is really no correlation between your power clean and FS, the second pull of the clean, where the power is generated, is almost exclusively hips and the front squat legs.
There IS a correlation between your front squat and FULL clean. They say that you should be able to full clean what you can front squat for a triple (assuming you can pull it high enough).
I'm not saying that squats won't help, but the reason oly lifters do a lot of squats is because they're squatting the weight up in competition. Many of them acknowledge that beyond a certain point, heavy squatting is a waste of time. If you can't pull it to waist (or even higher in the case of power cleans) height it doesn't matter how strong your legs are.
In other words, get your hips and back stronger, a big front squat is not important.