Inspired by previous studies and pioneers of the field, we present new results on an extensive Einstein, Podolsky, and Rosen (EPR)–Bell experiment using photons generated by parametric down-conversion, where one of the photons is deliberately phase-shifted. Our experiments show some surprising results for particular angles of this phase shift, where, for some states, the Clauser, Horne, Shimony, and Holt inequality shows no violations, requiring us to review our understanding of “entangled” states vis-à-vis the correlations obtained via experimental coincidence counts in agreement with quantum mechanics theoretical predictions. We give some possible explanations about the correlated states that show no violations of these inequalities.