I can't say that I agree with it, but I understand what she's trying to do. I would want to strongly deny that her reconstruction is the only one that gives the scriptures their proper place. I have personally spent hundreds and hundreds of hours working in the synoptic Gospels and on the synoptic problem specifically. I would have to say that Linnemann's thesis just doesn't stand up to any scrutiny.
If the Gospels were written by the men traditionally associated with them, then we have some different insights into the whole construction: Mark would have gotten his message largely from Peter. Matthew would have put his apostolic stamp of approval on Mark's Gospel by utilizing 90% of it for his own work. As an eyewitness, he would be affirming that Mark got it right. And Luke would have, as a historian, also affirmed the accuracy of Mark. Thus, we have essentially two of the synoptics from eyewitnesses (Peter and Matthew), and one from a rigorous historian. Yet, they agree. I think that it both honors the scriptures appropriately, shows that God works with human beings (that is, the scriptures are not just the Word of God but also are the words of men), and preserves a proper view of inspiration. And it becomes a threefold cord that is not easily broken. The problem with absolute independence is that it doesn't handle the data very well at all but becomes a faith-based supposition without regard for evidence. Christians already hold too many silly views that are based on leaps of faith; we don't need this one too.
The irony is that Linnemann has essentially followed her mentor, Rudolf Bultmann (she was a student of his several years ago), in basing her views on thin air. She has changed hats, to be sure--from liberal to near-fundamentalist--but the method remains the same.