I have the Shout Factory complete series set.
Alas though, I didn't buy it right away and when I did I discovered that it was a cost reduced version without the 7th case that had all of the bonus content (Which I've since realized is typical Shout Factory practice with their reissued complete...
I'm too lazy to go pop in some discs to double check, but I believe the cold open/teaser was only a season 1 thing for Leave it to Beaver.
Edit: Here we go with an example thanks to the Roku Channel.
https://therokuchannel.roku.com/watch/d910d480e837599fb0058cd893989587
It's of course...
That happened to Leave it to Beaver that Shout Factory put out. The transfers given to them from the network had the teaser misplaced, playing after the introduction.
I believe that the Universal set that used older tape transfers had the teasers correctly placed, if I recall old forum posts...