yes it is true but once you have driving card instead state ID no problem because on driving licence when you are permanent it is for 4 years validity unlike 2 years or else it is depand on your another status.on the other hand you can get state ID (most of american hold driving licence or state ID)with 24 dollers showing your PR proof etc,and you can hold it for that state on which, it is clearly noted that you are PR.
Police always verify driving licence or state ID number that are contain your whole information on system.
it is for New jersey state law and may be differ in other state regulation.