Found this explanation on a fencing website:
In foil and saber there is a rule called right of way, or priority,
which claims only one person may develop an attack at a time. If both
fencers are touched it is up to the referee to decide which fencer
will be awarded the touch and why. Difficulty arises when the
priority relationship between the fencers becomes confused. Each
person is struggling to gain control of the attacking initiation. If
sharp swords were used the truth would become apparent, but with dummy
tips understanding this is a subtle matter. The rulebook has a
standard explanation that the referee follows when arbitrating who
will be awarded a touch. However: each referee and each fencer may
judge events a bit differently. When a fencer does not agree with a
referee’s call there is little he can do unless the referee said
something which was unclear, or contrary to his own logic. It doesn’t
matter if both fencers think they performed in a way completely
opposite to the referee’s opinion - so long as the description of the
fencing phrase is clear the referee’s judgement is the final say in
the matter.
In the rulebook this decision is called a point of fact. There is no appeal for this. However; “if the referee is ignorant of or
misunderstands a definite rule, or applies it in a manner contrary to
the Rules, an appeal on this matter may be entertained.” (Fencing
Rules, 2000 Edition, t.122, t.96b) To make an appeal the plaintiff
should courteously inform the director that he would like to make an
appeal before the bout committee. Right then and there the bout
committee will decide on the issue. The fencer making an appeal on a
point of fact, or anything else for this matter should use discretion,
since both the referee and the bout committee can penalize a fencer
for an Unjustified appeal t.122, Delaying the bout t.31, or Refusal to
obey the Referee t.82, t.84.
So if I understand it correctly, the referee judged and called the point correctly, and since he followed the rule book it can't be challenged, despite the failure of the external equipment.
Edit: Just as a note, the rule book for USA Fencing is 230 pages long. That's about the longest rule book I've ever seen.