In many explanations of path tracers, such as http://www.thepolygoners.com/tutorials/GIIntro/GIIntro.htm, they apply direct lighting at each intersection point of the path. So at every intersection point, they trace a ray towards a light, and sample a different direction to continue the path.

Suppose I send out a ray that bounces three times and then hits the one light in the scene. Adding direct lighting at every bounce would be the same as not doing that, but having three paths, each leading to a light. Here the first path goes from the first intersection point to the light. The second path goes from the first to the second intersection point and then to the light. The third ray goes from the first to the second to the third intersection point and then to the light.

Is my understanding correct about this direct lighting approach? Does it sum up to the same end result?

If so, does this not lead to many more "samples" hitting a light than normally would, leading to incorrect lighting?