Do you need to show your ARC at immigration checkpoints?

Yes, I can now confirm this.

Yes, they warned me quite clearly when I applied for the ARC. They even reiterated the point.

Excellent procedure. Travelers are generally advised to have the passport copy anyway – it greatly facilitates, acc. to a US embassy officer I spoke to, emergency reissuance of a passport. Checked luggage gets lost often, though; I’d add another copy in one’s carryon. Copies are what, $1NT?