This may be overthinking the whole "gender difference" thing a teensy bit too much.

Random Fact: Red's team on HG/SS has the fully-evolved forms of Ash's team during the Orange Island Saga (coincidence or not is up to you), and his Pikachu had the 4 moves Ash's Pikachu knew at that time on the anime (As of DP144, Volt Tackle, Quick Attack, Thunderbolt, Iron Tail). And the Zoroark event on BW.

TL;DR The games and anime do share some Easter Eggs.