  The absence so far of any supersymmetric signals at the LHC pushes towards a
rethinking of the assumptions underlying the MSSM. Because the large missing
$E_T$ searches are inadequate to detect a LSP decaying within the detector,
R-parity violating supersymmetry is still a good candidate for low energy,
natural supersymmetry. We show that, in Froggatt-Nielsen-like models of
horizontal symmetries, specific textures for the R-parity violating couplings
are dictated by the symmetry, with the largest coupling involving the third
generation fields. Lepton number can be an accidental symmetry of the
renormalizable superpotential and barion number violation is given by a $\bar
u\bar d\bar d$ operator. The collider phenomenology then mimics the main
features of MFV R-parity violating supersymmetry. The LSP can evade current LHC
supersymmetry searches, is allowed to be well below 1 TeV and at the same time
all the constraints from proton decay and other low energy decays can be
satisfied; in particular, dimension five operators allowed by R-parity but
dangerous for the proton are under control, while neutrino masses are generated
by the Weinberg operator. Assuming sub TeV ({\it natural}) superpartners, we
obtain both upper and lower limits on the magnitude of the dominant R-parity
violating coupling: a lower limit of order $10^{-9}$ arises from null LHC
searches on R-hadrons and heavy stable charged particles, while a upper limit
of order $10^{-3}$ follows from constraints on low-energy flavor changing
neutral currents. Displaced vertices are predicted in the lower end of this
range.
