I have not heard that it is a thinning of the skin. I have heard that it is a broken blood vessel. Each blood vessel is in a tube form of layers to hold the blood between them. They appear kind of like a brick wall how one brick covers a half of two other bricks. All the broken capillaries are from what I have heard is where, for example, a brick is missing, and the blood can seep through the layers and spread under the surface.
I hope that makes sense, the best example I can think of is a brick wall.
However, I do know that people who are pale in complexion have thin skin and that people who are darker in complexion have thicker skin. I have also seen people with very dark skin, for example African, who do have broken capillaries. So on this example, I don't believe it is a thinning of the skin. However it would be good to see what some other people think.
