There is no answer to this question. The Op will never know if the estimate he received was legitimate or not because there are too many variables or possibilities. That is unless the problem recurs and the camera fails again- then he will know if they were right!
Here is my experience. In addition to my commercial photograher business, for about 25 years I partnered with a business that specializes in electric flas custom builds, modifications, and repairs. We shared premises with a camera repair shop- I can tell you stores and write a book
I di soothe minor repairs and were mostly involved in lamp head designs, and custom installation in studios, studios handling automotive advertis photography, and sports venues that our in house strobe installations.
Photographe would come in with faulty flash gear and complain, similarly to the OP, that the unts were sent to the authorized shop and the estimate was outrageously high. Here are the possibilities:
!. The folk's dogs the reais are not master technicians, but only parts changers. Rather later than troubleshooting a circuit board or point-to-point wire circuit, would simply replace the entire board or perhaps all the major components and charge accordingly. Our technician, at the time, had the knowledge and equipment to test each capacitor, chip, semiconductor, resistor, coil, and whatever and would only replace faulty parts., however, oftentimes, certain microcircuits and otere components were sealed, encased in epoxy, of undetermined electrical values, or not obtainable by non-authorized shops. A workaround would be the most costly than the original estimate.
2. The card mechanism (the door, springs, physical contacts) are mechanical, not electronic- it is subject to wear and tear, accidental abuse, dirt and dust etc. If this mechanism is totally integrated with a circuit board, the mechanical aspect cannot be separately repaired, lies an external switch or really, and the enter board needs to be replaced.
3. The cost of troubleshooting the board, in terms of labour, and replacing tiny components may exceed the cost of replacing the entire board. Some of the boards may be modular and impossible to individually repair.
4. Hopefull not, but there may be a possibility that once a camera is received for repair, at certain facilities, there is simply a minimum chare regarded of the issue.
OK, I know I am talking flash, not camera but my camera repair guy, that shared the shop, had simial issues quite frequently. The complexity and miniaturization of circuitry that is needed to support all the features in mode digital camera would certainly exhibit the formation difficulties in certain repar cases.
Sometimes, malfunctions in electronic devices are intermittent whereby the kida fix themselves and the recur, usually athe most inopportune times.
Of course, times have changed, especially in technology. Our shot had a miriad of old-fashioned test gear- precision voltmeters, multimeters, oscilloscopes, capacitor testers, specialized get to test chips, semiconductors and transistors, and more. Perhaps nowadays the maybe a poor that interphases with a computer, lie in your car that reads out all the diagnostics???
We closed the shop about 10 years ago. Sadly my partner in that business passed away. In the old days sometimes folks would bring in a faulty unit, we would pop the hood, perhaps change a fuse, hit the innards with some compressed air, give something a shot of contact cleaner and send it on the way with little or no charge.
In cases like this, we can only guess and speculate. I would lite to think that Fuji operates a hones repar facility.