not necessarily. There is an entire framework surrounding most "for hire" aircraft that outlines airworthy and unairworthy. The grey area for many operators is defined in a document called the MEL or Minimum Equipment List. These are items that when non functional...the aircraft could operate safely without...provided the crew heeds certain restrictions or takes some other action. IIRC this particular fuel gauge was already put on MEL. Each MEL is assigned a category and it is this category that defines the length of time this aircraft can operate with while having this broken thing. In most cases they are Cat C which is a 10 day reprieve. This system allows aircraft owners to get where they need to to fix the aircraft at the next opportunity. Or to continue operations while waiting for parts etc.
IIRC this gauge had been on MEL. The action the pilots where supposed to take was to manually determine fuel load by filling it before each flight. Problem with that is the only way to do it is to top off each time. Then you have an exact qty. There may be further restrictions about calculating fuel remaining and landing with a much wider safety margin etc.
In the case of this pilot I believe they had been operating this aircraft like this for so long they were surely not following the time restrictions on the MEL, probably gotten complacent regarding verifying fuel load etc. There are ways to "trick" an MEL.
If the pilot writes up the fuel gauge that is intermittent and they put it on MEL for 10 days but operations is trying to pinch pennies the following routinely happens:
Operations will put the aircraft in a down status for maintenance to work the fuel gauge. Operations may even inform Mx to not dig too deep right now because the MEL is still good for X number of days. If you cant find a simple fix after 8 hours of trying we will return the aircraft to service under the remaining time left for that MEL. Mx goes to work on this intermittent gauge and finds that it is actually working right now. Operations then says...well sign it off! Aircraft is returned to service with no discrepancies. Pilot comes in and flies the aircraft and after an hour of flight the fuel gauge ***** the bed again. He then writes up the intermittent fuel gauge for the 9th time and it is placed on a 10 day MEL. And the cycle continues until the pilots get so mad they threaten to quit or go to the FAA...lol.
This scenario happens at airports all over the US with operators on a budget. And occasionally smaller commuters. Almost never at places like Netjets or large commercial airlines like SouthWest.
What items are currently in this particular aircrafts logs will be of great concern to the investigators...if there are any.
Another thing they will look for....if they suspect a gearbox failure as others have said...gearboxes have something called "chip detectors". It is a small magnetic plug at the base of the gearbox oil sump. If the gearbox is beginning to show signs of premature wear...it will "make metal". That metal will be attracted to the magnet on the chip detector. Many chip detectors have an electrical circuit built in so that when metal sticks to the chip detector it completes a circuit and illuminates a "chip detect" annunciator in the cockpit. The pilot will then follow procedures in his emergency procedures manual regarding this warning. Even if the gearbox is smashed investigators may be able to tell quite a bit by looking at the chip detector and doing metallurgical analysis.
You havent lived until you are 120 miles out to sea in a helo and your main chip detector annunciator illuminates. Thats a quiet flight back to the first available landing spot.