Line Chart where two values are the same.

I am attempting to make a "timeline" the idea comes from another thread here - where you use a line chart and only use the X-Axis. You then add error bars and datalabels to make it look ok.

One stumbling block is that if two points have exactly the same value it appears that the chart only has one Point? Unless I am dreaming it appears that this is pictorially so and also the points collection count will be 1 less than what it should be?

How do people deal with this?