I believe he's shooting with a 5DmkIII, so increasing the ISO should be no problem at all.
Basically, every photo will have some degree of motion blur. Hand held and/or with a moving subject will be much worst that shooting still subjects on a tripod, but even then, it's almost impossible to take a photo that is 100%, absolutely free of motion blur. So the issue becomes, 'what is your acceptable level of blur?'. If you evaluate your images by loading them on the computer and zooming into 300%, then your acceptable level will likely be less than if you print out an 8x10 and hold it at arms length.
The old 'rule of thumb' about using a shutter speed that is 1/focal length (for hand held shooting), is based on acceptable sharpness. But with the way that most people evaluate their images these days, I actually teach my students to double that rule.
Of course, if you shoot with strobes as your main (or only) source of light, the exposure time from the burst of light will be much faster than your typical shutter speed, and that is what will help to freeze the movement and give you sharper images.