Homo Sapiens Heidelbergensis -> Homo Neanderthalensis?

[FeynmanMH42]

Both modern man homo sapiens and the Neandertals homo neanderthalensis are presumed to have evolved from Heidelberg man homo heidelbergensis. Because heidelbergensis is so physically similar to sapiens Heidelberg man was, for a long time, known as Archaic homo sapiens, in which case the Neandertals would also be a form of homo sapiens - DNA extracted from fossils shows this is not the case and the Neandertals were a separate species. After this discovery the use of the term Archaic homo sapiens for Heidelberg man seems to have fallen out of use. Now after researching specimens of Heidelberg and modern fossils I see almost no difference in the body shape(except that the Heidelberg/Archaic people were taller) and few differences in the head and face (a bigger brain.) These differences do not seem to me to be enough to make a new species - but the Neandertals clearly weren't homo sapiens.
Has no-one thought that maybe Heidelberg man was a form of our own species who evolved into Neandertals? In this case we didn't wipe out our ancestors or our cousins - we wiped out our children.
Is this possible?

 

[Phobos]

Some basic info which may or may not help here...
http://www.talkorigins.org/faqs/homs/specimen.html#archaics
http://www.talkorigins.org/faqs/homs/species.html#archaics

also, an old quote from a CNN article...(sorry, no link)

Many anthropologists believe H. heidelbergensis evolved into Neanderthals in Europe, but into modern humans, H. sapiens, in Africa. However, there is no consensus about the migration patterns of our primitive ancestors.