Without keys, how can one access the locked trunk of a 2003 Corolla, from the interior of the vehicle?
The latches on the back seats are for child seats.
I found a video for the 2007 model, but not the 2003.
On the 2003 Corolla the release for rear seats is in the trunk.
There are two knobs close to the hinges of the trunk.
Those are the rear seat back releases. If you push them toward the rear of the car they will pop and release the rear seat backs and you can fold them down and access the trunk.
This assumes of course that you have access to the inside of the vehicle.
Here is a PDF of the owners manual off the Toyota website. Page 30 has an illustration of the knob locations. You'll need to pull a top edge of the seat closest to the side of the car back enough to jam your arm into the gap to get access. If that doesn't work you may want to try the crack between the seats. The locking mechanism is in the rear of the seat back so either side will probably prove to be as difficult to access as the other.
I will add that I have managed to pull this off on a 2001 or '02. Either way, they are the same as yours.
Image of knob location
This video shows how to get into the trunk from the inside of the car. It works on 2003 Corollas as well: