Just like any other plane, you can fly a jet VFR as long as you maintain VFR rules. It is not a good idea, however. Being in a relatively fast-moving plane makes it more difficult to see and avoid other aircraft. I file a IFR flight plan for every single flight I make in a jet. Even on a repositioning flight such as KPHX - KSDL (12 NM apart) I do it. I did, one time, fill in for someone and SIC'd the repositioning of a Westwind in which the PIC did not file a flight plan. Frankly, I didn't really like it. It's just common sense to file, and controllers like to know you are coming, as well as know what you intend to do. But, again, there is nothing that says you can't go without a flight plan.
As for Wolcott, the thief, I looked him up out of curiosity. He holds a commercial pilot ticket and is type rated in the Westwind (IA-JET, and, for those that don't know what it is, that's a Westwind II pictured in my signature). However, the plane he "stole" apparently was a Citation VII (CE-650). I suppose he had some experience flying those, perhaps even taken a SIC course.
At any rate, he's a dummy and highly irresponsible. His flying career is most likely over.