We analyze the low energy implications of a flavor blind supersymmetric scenario (where the CKM matrix is the only source of flavor violation) in the presence of new CP violating but flavor conserving phases in the soft sector. We find that the best probes of this rather restricted scenario are (i) the electric dipole moments (EDMs) of the electron (de) and the neutron (dn) and (ii) flavor changing and CP violating processes in B systems, like the CP asymmetries in b→sγ and B→ϕ(η′)KS, i.e. ACP(b→sγ) and Sϕ(η′)KS, respectively. The non-standard values for Sϕ(η′)KS, measured at the B factories, can find a natural explanation within our scenario and this would unambiguously imply (i) positive and often large (non-standard) values for ACP(b→sγ) and (ii) a lower bound for the electron and neutron EDMs at the level of de,n≳10−28ecm. Moreover, we predict positive New Physics (NP) contributions to ϵK which could be welcomed in view of the recently lowered Standard Model value for ϵK. Interestingly, an explanation for the non-standard values for Sϕ(η′)KS can also naturally lead to an explanation for the anomaly of the muon anomalous magnetic moment. Finally, we outline the role and the interplay of the direct NP searches at the LHC with the indirect searches performed by low energy flavor physics observables.