  We consider the approximate minimization of a given polynomial on the
standard simplex, obtained by taking the minimum value over all rational grid
points with given denominator ${r} \in \mathbb{N}$. It was shown in [De Klerk,
E., Laurent, M., Sun, Z.: An error analysis for polynomial optimization over
the simplex based on the multivariate hypergeometric distribution. {\em SIAM J.
Optim.} 25(3) 1498--1514 (2015)] that the relative accuracy of this
approximation depends on $r$ as $O(1/r^2)$ if there exists a rational global
minimizer. In this note we show that the rational minimizer condition is not
necessary to obtain the $O(1/r^2)$ bound.
