Reflection as ambient lighting.

So it's my understanding that a reflection cubemap represents all the light coming in from surrounding objects, and that a really reflective surface is one with a great deal of shininess.

Given this idea, it seems to me that a reflection map should also affect non-shiny areas as well, just to a lesser degree. Trying this myself, it still seemed a tad too "shiny" on non-shiny areas.

Is my reasoning correct on how this should work? If so, how might I apply reflection maps as such a "global illumination"?

(I'm already using a custom coloured-specular lighting shader, by the way.)