Unreal;
I have noticed the same thing. The originals were probably installed with a squeezer machine that left that ring. I have seen several that did not have the ring so setting by hand will work. Did you see many that were painted?
You will need a semi tubular rivet set tool to set the rivet correctly.
for the best price I have seen on the rivet tool click here.
I really do not have a ton invested. I did pay way too much for the rivet set before I found them online. $4 a set or $1 a rivet including shipping is what I planned to charge. Send me a PM with how many you want. Anyone else need any?