It is possible that the GFCI device did not function as designed. Impossible to say without forensic analysis (which is kind of hard for random people on the internet). But it is quite likely that it did not fail:
GFCI protects exactly one thing - an imbalance between hot and neutral (on a 120V circuit) or between the two hots & neutral (on a 240V circuit). It does nothing to limit the total flow of current, as long as all of the current going through hot also goes through neutral.
A device on an ordinary circuit is designed to use a certain amount of power (current & voltage) and is designed so that under normal circumstances the heat generated will not cause any problems. But that doesn't mean problems can't happen. For example, a rolled up extension cord can easily overheat, even when used at the design (for unrolled) specifications. A toaster run in an enclosed space can overheat and easily start a fire. A heavy load (e.g., a full 15A) run for an extended period of time on a thin extension cord (perhaps designed & rated for max. 10A) can overheat the extension cord - causing it to melt - without tripping the breaker because the current is less than the breaker rating. In many of these cases, a regular breaker will trip once things start melting because then there is a short circuit == high current flow. In some cases - e.g., a 3-wire cord where the melting happens first between the ground wire & hot or neutral instead of between hot & neutral, a GFCI will trip.
Back to the specific example:
If everything is sealed sufficiently that, despite the outside being wet, no current is able to "escape", then the GFCI will not trip. However, overheating will gradually happen because mud is an insulator, leading to melting, short circuit and a regular breaker trip.