All you need is one exception to disprove his statement. If all three points are co-linear (all three of them are on the same straight line), then the statement is true. No other condition would make his statement wrong.
However let's look at this a little closer. Suppose H is not not the same line as J and G. Now what you have is an isosceles triangle. The two lines are equal GH = HJ but they are not situated so that H is the midpoint.
So his statement can be true, but it can also be false.
