In a recent paper we pointed out that the mixing of the light neutrinos with heavy gauge singlet states could reconcile the Z-pole data from e(+)e(-) colliders and the nu(mu) ((nu) over bar (mu)) scattering data from the NuTeV experiment at Fermilab. We further noted that the mixing angle required to fit the data is much larger than what would be expected from the conventional seesaw mechanism. In this paper, we show how such mixings can be arranged by a judicious choice of the neutrino mass texture. We also argue that by invoking the unification of the Dirac mass matrix for the up-type quarks and the neutrinos, the mass of the heavy states can naturally be expected to lie in the few TeV range. The model is strongly constrained by the lepton flavor changing process mu-->egamma which requires lepton universality to be violated in the charged channel.