  The spin-nematic phase is an intriguing state of matter that lacks usual
long-range dipolar order, yet it exhibits higher multipolar order. This makes
its detection extremely difficult and controversial. Recently, nuclear magnetic
resonance (NMR) has been proposed as one of the most suitable techniques to
confirm its existence. We report a $^{17}$O NMR observation of the reduction of
the local magnetization in the polarized state of the frustrated spin-1/2 chain
$\beta$-TeVO$_4$, which was previously proposed to be a fingerprint of the
spin-nematic behavior. However, our detailed study shows that the detected
missing fraction of the magnetization, probed by NMR frequency shift, is
thermally activated, thus undermining the presence of the spin-nematic phase in
the investigated compound. This highlights the importance of careful
considerations of temperature-dependent NMR shift that has been overlooked in
previous studies of spin nematicity.
