What you just described agrees with my definition. The ultimate goal of both teams was to end up with usable source code that is likely to be close or identical to the original used to create the binary. There is a slight difference in the IBM BIOS project in that, I think the goal was to create code which could not be claimed to infringe on the patents/copyrights of IBM. That last bit is an extension of reverse engineering, i.e. they reverse-engineered the binary (which took both decompilation and analysis) in order to create code which matched the same specification and wasn't outright "copied".
See the previous reply I made for links to discussion of what is usually meant by (software) "reverse engineering." But, like I said before, there probably is no "universally correct" definition, I am only describing it so that my previous comments can be understood fully.
You are right, that does agree with your definition. But, in my opinion, the reverse engineering was done only by the first team. They took the binary and constructed an understanding of the code. The second team just did basic software engineering from a spec. Your definition requires both teams and that's where your definition is too narrow.
See the previous reply I made for links to discussion of what is usually meant by (software) "reverse engineering." But, like I said before, there probably is no "universally correct" definition, I am only describing it so that my previous comments can be understood fully.