So, it means that the replacement process was not well documented. A repairman with all the information (like Authorized Apple Repair Service), can replace it. Something needs to be done in order to register the new official fingerprint reader. This was clearly not done by the unauthorized repair centers:they missed a step.
Now granted, they may not have known about the step that needed to be done, but they did not repair according to the required procedure. That's why they are not authorized, you see... As another comment under this story said begin with clear schematics and procedures. If those are present, a non authorized repair center could have done the work as required, without causing an Error 53. For all we know, many repair centers did... We just won't ever know because people using those phones are not complaining.
The fact that official channels can and do replace fingerprint scanners, means it's possible... and the unauthorized repair centers missed crucial information.
To use a car analogy that's like saying ford disabled your truck because the brakes were replaced - it's for your safety.
In a sense, yes... Though I'd more compare it to the "service" light that stays on, if you go to a 3rd party mechanic for an oil change and he doesn't know how to reset the service light back to "serviced". Granted, the service light here stops you from starting the engine, but that's mainly because it thinks you might have filled up the engine with water, and wants to prevent further damage (identity theft in case of a tampered fingerprint reader). Car analogies always break down somewhere.