However there is plenty of evidence to suggest that witness statements are often not an accurate reflection of events, or, for that matter, a reflection of the account of the witness.
This is absolutely right. There has been research over the years about this. Most statements in criminal matters are written by police officers and tend to reflect what the officer wants them to say. I have cross examined many witnesses over the years on inconsistency between their statements and their oral evidence. Usually I found that the police wrote the statement and that the witness barely if at all read it before signing. Even if they know something is wrong they will ofton not want to argue the point with the police officer.
Interestingly, in Scotland, the defence always take their own statements from witnesses, even prosecution witnesses and statements given to the police cannot be used to cross examine a witness as the courts presume that it is written in the police's words and not the witnesses (if this procedure has changed I apologise to any Scotish lawyers who may be reading this!).