Scott,
Most of them do have the belt - I have no clue how I came across this one with the snap, but it's original. In fact, it basically doesn't look like it was ever used. It has the 1960's Brunswick logo with the "crown". I didn't even know Brunswick made cases into the 1970's. George also used Palmer cases and gave those with his cues for many years.
Check this out. During the 1950's and into the 1960's, Brunswick made two different styles of cases, 1) the Expert, which is a little thicker and has some padding and a luggage style handle, and the more common one 2) the Aristocrat. This is from the 1952 catalog.
http://www.palmercollector.com/Brunswick/Brunswick_1952_page_13.jpg
I wish you still had every old cue you owned. I now have 4 or 5 Eddie Laube's that you introduced me to. They're pretty cool cues.
Chris