It's not just about Greeks wielding their spears over-hand; Near Eastern infantry formations, later Egyptian infantry, and especially Persian shield-bearer contingents formed a shield-wall where spears could be used over-hand. All of these formations remind of an Argos phalanx. This technique of using the spear largely applied to the majority of cavalry forces as well if they ever had spears to begin with; A notable exception could of course have been the Lydian heavy cavalry who were noted for their long lances, perhaps wielding it like a xyston.

There were certainly many situations even a large lance, such as the kontos, could have been used over-hand as well, however it appears to need a few prerequisites in order to facilitate such usage; The late Sassanian bas-relief of Tâq-î Bûstân shows a clibanarius wielding its kontos in such manner. However, the feet are damaged, making it impossible to make out with any greater accuracy if the rider is wearing stirrups; The Pûr-î Vahman bowl shows stirrups, and a similar posture with the knees slightly protruding in a sharper angle; Previously we see Partho-Sassanian chivalry riding in the "ballerina"-posture where the feet droop. Nevertheless, the technique of stabbing with the spear, given the situation, even on horse-back prevailed for a long time.

Sarcasm is pretty damn spot-on.