In search of the potential realization of novel normal-state phases on the surface of Sr2RuO4 - those stemming from either topological bulk properties or the interplay between spin-orbit coupling (SO) and the broken symmetry of the surface - we revisit the electronic structure of the top-most layers by ARPES with improved data quality as well as ab-initio LDA slab calculations. We find that the current model of a single surface layer (surd2xsurd2)R45{deg} reconstruction does not explain all detected features. The observed depth-dependent signal degradation, together with the close quantitative agreement with LDA+SO slab calculations based on the LEED-determined surface crystal structure, reveal that (at a minimum) the sub-surface layer also undergoes a similar although weaker reconstruction. This points to a surface-to-bulk progression of the electronic states driven by structural instabilities, with no evidence for Dirac and Rashba-type states or surface magnetism.