At a 'headline' level your reasoning seems correct for the two reasons you identified AND that any design developed by the Contractor has to comply with Works Information under clause 21.2, regardless of whether the PM accepts it or not.
I say 'headline' level though as my experience of these things is that they are far more messy than they first appear !
I say 'headline' level though as my experience of these things is that they are far more messy than they first appear !