Using (63,65)Cu nuclear magnetic resonance in magnetic fields up to 30 T, we study the microscopic properties of the 12-site valence-bond-solid ground state in the "pinwheel" kagome compound Rb(2)Cu(3)SnF(12). We find that the ground state is characterized by a strong transverse staggered spin polarization whose temperature and field dependence points to a mixing of the singlet and triplet states. This is further corroborated by the field dependence of the gap Δ(H), which has a level anticrossing with a large minimum gap value of ≈ Δ(0)/2, with no evidence of a phase transition down to 1.5 K. By the exact diagonalization of small clusters, we show that the observed anticrossing is mainly due to staggered tilts of the g tensors defined by the crystal structure and reveal symmetry properties of the low-energy excitation spectrum compatible with the absence of level crossing.