There are faults IDs that trip if certain telemetry goes outside of a normal range. If a safemode were to occur, we would investigate which faults tripped and at what time, and use those to construct a "story" of what happened on the satellite before it entered safemode. We're also constantly recording every telemetry that comes down, so we could reference any telemetry we wanted as far back as months in the past.
To your point, yes you're correct. The cause of the safemode is much more interesting than the fact we entered it.