I had a case like this.
The CMC wanted to go to court because they knew how Courts worked. Almost insider knowledge. The PI company wanted to settle due to the expense of a court case – time, solicitor and barrister costs etc.
I wrote to the client with the FOS leaflet and advising that the FOS was a free service to them. Going to court did not increase their chance of success etc.
Now that the CMC should be regulated by the FCA perhaps you could raise it with the FCA that the CMC has chosen to go to court rather than FOS. particualrly if the case looks odd. Then the FCA can look into the matter.
Good luck.
TC