A couple things first. The time you put on your timecard, did you perform work for those four hours or were you told to be around your phone if the station needed to call you It sucks to have to be chained to the station during your time off, but if you weren't actively engaged in work, you may not be eligible to get money for time you were told to be on standby.
We have on-call at our place and we don't get paid for being scheduled on-call but there is a guaranteed minimum number of hours to be paid if we do get called.
So if you are in a union, that will determine how/if you are paid and the laws in the state you are working in effect how/if you are paid.
If you were actively performing work, then I doubt any state would have a law that says you wouldn't be paid. If you were working on your own and put in time you'd still have to be paid, although, if the overtime was not authorized you could be liable for discipline, but they'd still have to pay you for work performed.
In short, if you were working you should get paid. If you were told to be available but didn't perform work, you may not be eligible for pay even though you had to work your plans around maybe getting called in.