"Even if that scenario is a valid reason not to talk to the police, it wouldn't be possible in a courtroom, where all of your answers are recorded, and it will be obvious if someone is trying to distort the meaning of something that you said earlier."
No. That's just not right.
In 1992 I spent several hours giving testimony in a trial involving murder. The defendant in this trial was NOT the individual that actually pulled the trigger but instead was seen as being in a "leadership" role. My testimony involved his character and whether or not it was in his nature to give such an order for murder - or if the killer acted without instructions and on his own.
During my testimony, I repeated stressed that it was not in the character for the defendant to give such an order; he was a pacifist who had often walked away from provocations and even mediated internal disagreements within the organization. It was clear to me, and I did my best to articulate it to the court, that giving such an order was so far outside of the defendant's character that I found it impossible to conceive he would do such a thing. I also gave testimony as to the personality of the actual killer, who was well known to me as a bad-tempered, short-sighted, and unruly fellow.
When I finished my testimony, the defendant's family thanked me for my supporting testimony. However, in the end, my testimony was twisted around and used as a central part of the prosecution's argument to convict the defendant - in essence my mention of his prior mediations and the absence of any mediation in the matter at trial was distorted to imply that by his lack of mediations he was tacitly giving an order. Despite everything being on record, and having been said in front of the jury, my meaning and intent was distorted into exactly the opposite of what I intended to convey. Anyone that thinks such distortions, "wouldn't be possible in a courtroom", simply has never been involved in a serious trial.
To this day, more than 20 years later, that defendant is still in prison serving a life sentence. His every attempt at an appeal has failed. Meanwhile, one of the two men that actually pulled triggers has been released (because he 'accepted responsibility for his crime, thus indicating successful rehabilitation').
Some might claim that my personal anecdotal evidence represents something uncommon - I wish I could believe that - but even so, when a claim is made that something "wouldn't happen" it only takes one example to prove that it certainly can happen. If I had never talked to the police, that defendant would never have been convicted.