The rules you posted are pretty much correct. I'm actually surprised you need to have them though, and can't help but wonder how there was confusion about this.
If I make a bet and you call me, I need to show my hand in order to win the pot. If I choose not to, that's fine, but I am then conceeding the pot to you.
No player ever really HAS to show their cards - they simply need to get them into the muck before anyone asks to see them (which is a pretty tacky thing to do anyway, unless you suspect collusion, of course).
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