No, it's not inconceivable that they are at fault, but they will be blamed regardless.
Oh, and if the trasnponder wasn't lit, then how did ATC know the altitude?
Oh, and if the trasnponder wasn't lit, then how did ATC know the altitude?
If they were close to a radar facility they could have gotten a secondary return, or "skin paint". This is not likely though--they probably would've had a second transponder and ATC would've brought the problem up to them long before this. Besides, they are not legal to fly at that altitude in RVSM airspace, which I'm certain this was, without an operable transponder with altitude reporting capability. If ATC allowed them to continue in RVSM airspace without an operable altitude reporting capability then they are culpable.
RVSM Requirements
The following requirements have to be fulfilled to get an RVSM STC:
Two independent altitude measurement systems meeting the system error requirements.
One automatic control system keeping the aircraft altitude within ±20 m (±65 ft).
One altitude alert system with limits ±90 m (±300 ft).
One secondary surveillance radar (SSR) altitude reporting transponder.
RVSM compliant avionics configuration.