Hi John,
As Satish said, it's right, but not only in the Factory Act. It's applicable in all labor laws. In fact, most organizations mention this clause (that a particular employee will not be eligible for dual employment without correct organization permission) in their Offer Letter or Appointment Letter the moment they appoint anybody.
However, there are some legal ways to engage in dual employment in some cases.
Regards, Tushar Swar.