Earlier quoted context omitted.
It doesn't seem so unlikely to me. Supply chains are long and parts are bought in bulk. I think it's likely that the parts for the ECUs, including boards with chips containing the older firmware, are warehoused where the ECUs are assembled. The ECUs are probably then bought in bulk and warehoused where the planes are assembled. The paperwork for the plane probably includes the ECU serial numbers, but it probably does…
I think you underestimate the tracking done in commercial airplane manufacture. I believe the source of every rivet is well-known. And how many planes do they make? Many parts are likely manufactured as needed, one at a time.
As far as JIT manufacturing, that's certainly the case for bigger parts and systems, but it sounds like the ECTs are replaceable so they probably have backup replacements stocked near most major airports. (Assuming it's a part that can be replaced during routine pre-flight maintenance.) And the components that go into the ECTs are almost certainly produced in large batches rather than continuously.