He's relying on isospin symmetry.

The integrals you exhibit are for the proton, but the the form factors in the ratio are proton in the denominator and neutron in the numerator.

The claim is that the up-distribution of the proton is a good proxy for the down-distribution of the neutron and vice versa, and that the sea distributions are identical.

That is \begin{align*} u^{en}_V(x) &= d^{ep}_V(x) \\ u^{ep}_V(x) &= d^{en}_V(x) \\ S^{en}_V(x) &= S^{ep}_V(x) \end{align*}

None of those things is exactly true, but they're pretty good approximations at low momentum fraction.

He's relying on isospin symmetry.

The integrals you exhibit are for the proton, but the the form factors in the ratio are proton in the denominator and neutron in the numerator.

The claim is that the up-distribution of the proton is a good proxy for the down-distribution of the neutron and vice versa, and that the sea distributions are identical.

That is \begin{align*} u^{en}_V(x) &= d^{ep}_V(x) \\ u^{ep}_V(x) &= d^{en}_V(x) \\ S^{en}_V(x) &= S^{ep}_V(x) \end{align*}

None of those things is exactly true, but they're pretty good approximations at low momentum fraction.

With those substitutions, the identity should be obvious.