Well either the female presenter in the recent podcast is lying (she came over as sincere in her beliefs to me) or you have misunderstood. I listened very carefully to the podcast, pausing to make notes, and the support group put together the submission with the lawyer simply endorsing it.
They discuss this at 1:24:36. It is Philip Walker who says the CT put the submissions together and get the lawyers to approve it, then put it in to the CCRC, but I honestly think that can be interpreted in different ways. It's just words on a podcast. It could mean the CT do everything and the lawyers just read it for legality. Or it could mean that the CT do all the leg work and the lawyers then prepare and advise on the submissions (which I think is more likely).
I still say that I'm not inclined to rely on anything the CT say about the evidence or what they have done. They are campaigners, not lawyers, and during the podcast both Philip and Yvonne use legal jargon loosely and incorrectly. For instance, Philip talks about 'exculpatory evidence', which I doubt actually exists. I think he very likely means evidence that the CT believe casts doubt on the safety of the convictions.
More importantly, although the CT outline the submissions topically, they don't go into detail about what evidence they have.
I am inclined to wait before casting judgement on any of this, one way or the other, and I think this discussion on the thread is becoming a bit circular.