Key agreement protocols are a fundamental building block for ensuring authenticated and private communications between two parties over an insecure network. This paper focuses on key agreement protocols in the asymmetric trust model, wherein parties hold a public/private key pair. In particular, we consider a type of known key attack called key compromise impersonation that may occur once the adversary has obtained the private key of an honest party. This attack represents a subtle threat that is often underestimated and difficult to counter. Several protocols are shown vulnerable to this attack despite their authors claiming the opposite. We also consider in more detail how three formal (complexity-theoretic based) models of distributed computing found in the literature cover such attacks.