Is your user of the paint-box using it's external sync input. If I remember, the paint-box can receive a sync to lock onto your studio's master reference for use in a studio mixing console environment, like many pros who use the Video Toaster who may use a master sync reference generator for all their gear. The photo you are giving us looks like the external sync locking input is loosing lock part way down the screen.
I've seen this once on an old high end Amiga NTSC genlock where the source sync was the wrong amplitude. Funny that the cheaper crummy genlocks had no problem with the locking, but the pro-gear was really tight on studio specs.
Note1: if he was feeding a pal sync into a RGB+Sync monitor, the vertical may go out of whack, but, the horizontal shouldn't go all swiggly.
Note2: if he is feeding the Amiga Video Toaster and the paintbox unit's output sync isn't perfectly timed, even though it is set to NTSC, the Toaster will loose horizontal lock exactly as you see. In this case, you do need to feed the paintbox a reference NTSC sync to ensure it's internal clock is dead on. (Assuming the paintbox's internal video clock generator is a PLL oscillator which may have too large a drift factor when not receiving an external sync. (It is not that the output of the paint-box is swiggling, it's that it is just too slow or too fast for the crystal PLL tuned clock in the VideoToaster to hold onto and the result is what you see coming out of the Video Toaster)). I've seen this before feeding a Video Toaster with a color bar generator who's video source was slightly off due to the wrong loading capacitors on the reference 27MHz crystal. (Yes, it was my design of a color bar generator...)