Looking a little better at the OP's original question, I could probably do a better job of answering than my first post...
Yes, it is down to the camera. Your sensor is 'hidden' behind a pair of sliding shutter curtains, and when you take a shot, the first curtain drops and reveals the whole sensor.
After the exposure time, the second curtain drops (to shield the sensor) then both curtains move together - still closed - back to their original position.
However, at some point, usually around 1/100 to 1/250s, the curtains can't move fast enough to completely open, wait for the exposure time, then close. So, instead, the first curtain opens a little, then the second curtain starts to move and follows the first across the frame. The end result is that every part of the frame is exposed for the right amount of time - e.g. 1/1000s - but it's been exposed as a rolling horizontal band that's swept down the frame.
As has been pointed out, a pulse from a flashgun is really short, so if you take an exposure of, say, 1/100s, the first curtain drops, at some point the flash fires, then 1/100s later the second curtain ends the exposure.
If you're over your camera's sync speed (faster than 1/250s for your 60D) then the flash pulse will happen at some point when your two shutter curtains are moving together across the frame. The end result is that only a portion of the frame gets light from the flash.
With a HSS capable flash, the flash instead emits a series of smaller pulses while the shutter curtains move, thus providing light for the whole exposure.
Hope that helps.