Right
卑 supplies the sound — bēi shifted to pí, regular b/p labial alternation.
卑 originally pictured a hand holding a ladle, a marker of a low servant's role; that meaning doesn't carry. Same phonetic family:
啤 (beer),
婢 (slave-girl),
牌 (sign/plaque),
碑 (stele). Common compound
脾气 (pí qì, temperament) reflects the classical theory of the spleen as the seat of mood and disposition.