This matters mostly because of the term "non-repudiation." Like "trusted," this term is taken from the literature of academic cryptography. There it means something very specific: that the digital-signature algorithm is not breakable, so a third party cannot forge your signature. PKI vendors have latched onto the term and used it in a legal sense, lobbying for laws to the effect that if someone uses your private signing key, then you are not allowed to repudiate the signature. In other words, under some digital signature laws (e.g., Utah and Washington), if your signing key has been certified by an approved CA, then you are responsible for whatever that private key does. It does not matter who was at the computer keyboard or what virus did the signing; you are legally responsible.