As indicated: for the first trial, the police seemed to feel that Jyoti Patel was a more direct witness, with almost a line of sight on the accident, so that's who they chose to take a statement from. Then that's what Lee used and legally had to make accessible to Jenkins.
Lee almost immediately discovered there were conflicts in Ahmed Patel's statements, but since they didn't serve Lee's purpose in trying to build and win his case, there was no reason for him to bring them up. Had Jenkins discovered them on his own, Lee would have tried to diminish their importance in the first trial.
And when Carleson discovered the inconsistencies in Ahmed Patel's statements and used them in the second trial, Lee had the good sense not to protest and, instead, to concentrate somewhere else.
Also, I don't think the police were necessarily trying to interfere. This book really isn't about that or about conspiracies. I think the police were trying to get the clearest evidence with their own limited resources and time.