This work aims at presenting an alternative approach to the long standing problem of the B(E2) values in Sn isotopes in the vicinity of the N=Z double-magic nucleus 100Sn, until now predominantly measured with relativistic and intermediate-energy Coulomb excitation reactions. The direct measurement of the lifetime of low-lying excited states in odd-even Sn isotopes provides a new and precise guidance for the theoretical description of the nuclear structure in this region. Lifetime measurements have been performed in 105Sn for the first time with the coincidence Recoil Distance Doppler Shift technique. The lifetime results for the 7/2+ 1 first excited state and the 11/2+ 1 state, 2+(104Sn) ⊗ ν1g7/2 multiplet member, are discussed in comparison with state-of-the-art shell model and mean field calculations, highlighting the crucial contribution of proton excitation across the core of 100Sn. The reduced transition probability B(E2) of the 11/2+ 1 core-coupled state points out an enhanced staggering with respect to the B(E2; 2+ 1 →0+ 1 ) in the even-mass 104Sn and 106Sn isotopes.