A note on $sigma$-algebras on sets of affine and measurable maps to the unit interval

In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the $sigma$-algebra induced by the evaluation maps. The author asserts that, under the assumptions given in the paper, the two $sigma$-algebras coincide. We give examples contradicting this statement.