After re-reading my post below I had a moment of syntactic beguilement at my own use of the was that what X was that X construction: Our group consensus was that what he really meant was that a linguistic topic was "interesting" if it helped him make his argument.
I imagined four relevant sentences; two grammatical/acceptable and two ungrammatical/unacceptable according to my own most excellent judgment*. My challenge to you, dear reader, is to explain why sentences (1-2) are grammatical/unacceptable and why sentences (3-4) are ungrammatical/unacceptable.
- our consensus was that what he really meant was X
- our consensus was he really meant (that) X
- *our consensus was what he really meant (that) X
- *our consensus was he really meant was X