Kommisar: you might be surprised at how many of the "big names" used Falck tubing, but primarily as a "mixer" as in the occasional tube to make up a set or very typically for stays and steerer...even though there'd be a Columbus decal on the frame. Falck got absorbed into the giant Mannesmann tubing behemoth, AFAIK. It's rare to see a Falck tubing decal (indicating an entire Falck tubeset) but I've seen a handful.
As to the Cinelli sleeve, you can't really see it cause it's so cleanly done, but you get an idea from this shot of the extra thickness at the top of the seat lug...it's certainly something a caliper would show, and it's done for the classic fastback cluster, it wouldn't be required to have the extra metal there with regular side-brazed stay caps. (Pic is from the CR main site> Italy>Cinelli)
check loosescrews.com for those DO thingies, they have them cheap