2003 Toyota Camry low thumping noise from rear

How far did someone go with the inspection? Did they pull the rotors off? One common thing to look for is raised spots of rust on the back of the rotor mounting surfaces. Those form where water gets in through the wheel bearing access holes. That rust needs to be scraped off before the rotors are mounted on the brake lathe to be machined. If they are not removed the rotor could wobble on the lathe and a warp will be machined into the rotor. It's also possible for those spots to get stuck between the rotor and hub when the rotor is reinstalled in a different orientation. That will also make it wobble on the car. You'd find that by measuring "lateral runout" with a dial indicator. The noise you described could be due to the wheel and tire wobbling and the tire is scrubbing back and forth on the road, or it could be due to the caliper sliding back and forth when no brake grease was used on the mounting points.

If the rotors were not machined there is going to be a ridge of rust on the outer edge and the inner edge, and the new linings could be rubbing on them. That will wear away over time. That's not easy to spot during a visual inspection.

It sounds like you have the location of the noise source identified already but there's a tool you might consider trying. It's called the "Chassis Ear". That's a set of six microphones, a switch box, and head phones. You clip the microphones to suspect parts, then switch between them while driving and listening. I used one at times when doing suspension and alignment work and trying to find the source of squeaks and rattles. You might find one of these tools at an auto parts store that rents or borrows tools.

One strange thing I've run into multiple times is a squeaky wheel cover. In fact I worked on a huge motor home tonight that has one making noise when the wheel is turning and flexing. A light coating of grease where it attaches will solve that.

If you replaced the rotors three months ago and they were made in China, they are likely warped. When we make parts out of cast iron, we throw them outside for three months to "age" before they get their final machining. There's nothing wrong with Chinese rotors but they cast 'em, pack 'em, and ship 'em, then they age on your car. If warpage develops usually all that's needed is a light machining and they'll be fine. You won't find that by measuring for thickness variation with a micrometer. You have to snug the lug nuts, then measure the runout with a dial indicator while you spin the rotor. If you do find some runout, measure it on the center part that contacts the wheel. If you find runout there too it's not due to a warped rotor. It's due to rust or scale falling between the rotor and hub. That has happened to every brake specialist at some point.

Was that a single flat spot or a bunch of them evenly spaced all the way around? A single one would be from skidding the tire. Multiples could be from a weak strut but if the tire on the other side has the same wear pattern it is from incorrect "total toe". That is one of the basic alignment angles and has to do with the way the pair of tires are steering.