Griffith's 1987 book correctly states a totally reasonable hypothesis, that the neutron's core is positive. Here's a simple model which probably goes back to Fermi: the neutron ought to spend part of its time as a virtual proton-$\pi^-$ pair, in a strong-interaction analog to the photon spending part of its time as an electron-positron pair; since the proton is heavier than the pion, you'd expect to find the positive charge concentrated near the neutron's core.
Wikipedia correctly observes that Miller shows, using data that did not exist in 1987, that the electric and magnetic form factors required to describe scattering from nucleons at different momentum transfer don't describe a charge distribution with a positive core. The simple virtual-$\pi^-$-cloud model is wrong. A better model for the neutron has a negatively-charged core and a slightly negatively-charged halo, with the charge cancelling due to a positively-charged layer in between.
The quarks that make up the neutron carry different fractions of the neutron's momentum. The most likely fraction of the momentum to be carried by any particular quark is $x=\frac13$, since there are three valence quarks. However these fractions fluctuate, as quantum-mechanical properties do. Apparently the data show that the neutron's $d$ quarks are more likely to carry more of its momentum (large $x$) than its $u$ quarks. The high-momentum quarks, with more relativistic energy, are more likely to be found near the neutron's center of mass; since these are more likely to be $d$ quarks, the neutron's core is negative.