I understand that the following relation exists:
$\eta(s) = \left(1-2^{1-s}\right) \zeta(s)$
and from this question:
What are the hypothetical zeros of the Dirichlet eta function
that the Dirichlet eta function zeros "are precisely the zeros of the zeta function", but then I am confused by this paper:
https://arxiv.org/abs/1201.1810
The author claims to "show that the Dirichlet eta function has no zeros in the critical strip off the critical line, consistent with the Riemann hypothesis."
My question is how is this only consistent with the Riemann hypothesis, or in other words, how does this result not imply the Riemann hypothesis?