We analyze simulated streaked valence band photoemission with atomic streaking theory-based reconstruction methods to investigate the differences between atomic gas-phase streaking and valence band surface streaking. The careful distinction between atomic and surface streaking is a prerequisite to justify the application of atomic streaking theory-based reconstruction methods to surface streaking measurements. We show that neglecting the band structure underestimates the width of reconstructed photoelectron wavepackets, consistent with the Fourier transform limit of the band spectrum. We find that a fit of Gaussian wavepackets within the description of atomic streaking is adequate to a limited extent. Systematic errors that depend on the near-infrared skin depth, an inherently surface-specific property, are present in temporal widths of wavepackets reconstructed with atomic streaking theory-based methods.