It's not really a myth, as it comes from the account of Bernal Diaz del Castillo, who was part of Cortes' company. After a battle with the Tlaxcalans, he wrote:

When, therefore, the attack commenced, a real shower of arrows and stones was poured upon us; the whole ground was immediately covered with heaps of lances, whose points were provided with two edges, so very sharp that they pierced through every species of cuirass, and were particularly dangerous to the lower part of the body, which was in no way protected.

He makes further reference to the penetrating power of the tepoztopilli (a long spear), writing:

The pikes are so very sharp and hard that they will pierce the strongest shield, and cut like a razor....

Diaz del Castillo himself had very personal experience with these spears, not just in combat before and during the Battle of Tenochtitlan, but also after. While on campaign in Chiapas, he recorded that

I myself received a heavy thrust from a lance, which completely pierced my armour, and I should certainly have lost my life on the spot if my cuirass had not been strongly quilted with cotton.

So, the source (or at least a source, I am not responsible for wild speculation on the interwebs) is the firsthand account of a Spanish conquistador.