There are, for sure, different interpretations of 'specular', especially when applied in different situations. My previous post was about reflecting surfaces ('specular reflections'), and Claire's post is about print values ('specular highlights') - '...a specular highlight is direct sunlight hitting polished chrome or other metals or glass and it is intended to be printed paper white in the print...'
For Claire's definition, with which I have no quarrel, there is indeed no reason to meter for the 'specular highlights'.
But don't we need some way to describe the bright, directional mirror-like reflections from non-mirror surfaces when we want them to record detail? The practical importance of the apparently academic distinction is a result of the assumptions made about the limits to the range of surface reflective index when using an incident meter. 'Specular' reflections may lie outside this range, and we may wish to record detail in them. If we wish to record detail in them an incident meter cannot, on its own, indicate the exposure required because the ratio of incident to reflected light is unknown.
How does that sound?
PS. "Lambertian". That's the name of a totally diffuse surface with equal intensity reflections over a hemisphere.