We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, Invent. Math. 150(2002), 185-217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 174(2008), 139-163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.