Precisely.
I always thought the same thing and taught my son that; UNTIL I became a court reporter.
Now I tell EVERYBODY not to say a word until you have legal representation.
And I do mean even in car accidents!
Yes, and the minute you walk in with legal representation or say you will meet with them and talk WITH legal representation, the police file the charges (because you look guilty). The School Administration says you can't have a lawyer present, because they'd have to have one present, too (so, like, go ahead -- I'm sure you have one on retainer), and you're screwed either way, but at least your child didn't make a statement against their own best interests.
I'm telling you, any adult worth his salt can have your scared kid admitting to being on the grassy knoll in Dallas by the time they are done (and that was 20 years before your kid was born). We would have solved the conspiracy long ago, had we been able to interrogate kids.