An attosecond streak camera holds the promise of time resolving the dynamics of photoionization with a few-attosecond accuracy. But can the attosecond measurement be disentangled from the process it measures? We address this question by deriving simple closed-form analytical expressions for the measurement-related apparent time delays in photoionization, associated with the application of the attosecond streak camera and/or resolution of attosecond beating by interference of two-photon transitions techniques. Our analytical results are accurate on about the 1 asec level and show that both intrinsic and measurement-induced delays depend on the same scattering phase and are, therefore, not independent. We also suggest a procedure for extracting intrinsic time delays from the measurement and a possible resolution of the controversy caused by the experiments of Schultze et al. [Science 328, 1658 (2010)].