In this paper, the multiple-access channel with an external eavesdropper is considered. From the perspective of the trustworthiness of users, an overview of existing secrecy criteria is given and their impact on the achievable secrecy rate region is discussed. For instance, under the assumption the eavesdropper has full a priori knowledge of the other users' transmit signals, the mixed secrecy criterion requires the information leakage from all transmitted messages individually as well as jointly to be small. This is a conservative criterion useful for scenarios in which users might be compromised. If some of the users are trustworthy, however, the secrecy criterion can be relaxed to joint secrecy resulting in a significantly increased rate region. As this indicates there is a trade-off between the choice of the secrecy criterion and achievable rates, the question is posed as to whether the criterion can further be weakened to individual secrecy, which would be desirable for scenarios where users are guaranteed trustworthy.