An employer cannot refuse to pay the salary that is due to the employee working under him for any reason.
The aggrieved employee can first issue a legal demand notice demanding his pending salary after which he can approach the labor court with an application to get his grievances redressed.
The company is wrong to say that the private company has governed by a different law.
All the companies in India are governed b y the Indian laws and no one is exempt from that.
Therefore you may proceed as suggested.