Wilson and Alexis can both by correct if the the function is a parabola. It can have zeroes at points x=-1, and x=1. Thus, the average rate of change between the two points would be zero because the y values do not change as they are both zero. In this way, Wilson is correct. Alexis can be correct because the parabola can have it's highest point at its vertex between the two points. It would count as a turning point because the function would increase and then decrease again.
If the function is a parabola, with vertex on x= 0, then the average rate of change of the function on {x: -1<x<1} is 0, because the graph is symmetric. There is also a turning point at the vertex.
