Yes, discs get hot, sometimes very hot, and yes, sometimes hot enough to cause braking issues. No, that heat will not be sufficiently transferred (through the 'spider' on the rotor and through the hub's disc boss and out the hub's flanges) to the spokes such that it would cause the metal of the spokes to weaken... that's absurd.
Disc brakes DO, however, put a load on the spokes in a way that rim brakes do not - rim brakes stop the rim directly, while disc brakes stop the rim by exerting force on the hub which pull on the spokes to stop the rim. Enough to break spokes? Maybe over the medium term after many miles. If that is how that pro's spokes broke then it is an issue of not replacing the wheels or spokes soon enough, or of some other problem with the wheel build or configuration. It's easy to forget that lots of riders in that event (and many other events and grand tours) use disc brakes, yet only one person complained of the disc brakes causing spokes to fail.
Perhaps the rider got to the finish line and the team mechanic was embarrassed that a bike in their stable had a problem, and rather than admit the wheels didn't get the attention they needed before the race, or that the wheels given to the team by a sponsor had a failure, used the excuse that it was the discs' fault,