I would agree with you but his girlfriend is just nauseous, not even throwing up. I would not consider that severly ill. The second day on my cleanse was the roughest day of all and after that it was relatively mild ups and downs so she is not alone in her second day feeling pretty sheety, many people experience this...
Certainly I think she should continue under the circumstances since the camaraderie of her boyfriend will help both be successful in their cleanse and by tomorrow the nausea will most likely pass.