QGIS » QGIS Application

The problem here is that the behaviour of QGIS is different from what you expect. The behaviour is consistent, but the edges are defined different, like this:

0     white       <= 0
0.01  light grey  0 < .. <= .01 (essentially 0.01)
0.02  med grey    0.01 < .. <= .02 (essentially 0.02)
0.1   dark grey   0.02 < .. <= 0.1 (or 0.03 to 0.1)
2     dark grey   0.1 < .. <= 2 (or 0.11 to 2)

I've improved the automatic labels to make the ranges more clear, see https://github.com/qgis/QGIS/pull/2979

However, I noticed that the behaviour is not consistent with the gradient editor, which adds an extra class at the end, like you did.

If the type of breaks that you expected is also more common in other software, or otherwise more logical I think it makes sense to discuss if the renderer should be changed.

In the source documentation of QgsColorRampShader::exactColor() it says "Assigns the color of the lower class for every pixel between two class breaks.". That suggests the behaviour William expects actually also is the intended behaviour and the implementation is indeed wrong. Still the question is whether to fix the implementation or keep it and make it more clear what happens.