The earlier poster who said it was a fan club of some sort sounds plausible. I had also mentioned earlier in this thread "Race to Witch Mountain" which opens in theaters that same week.
Here's some other speculations of a few noteworthy things that have a 1986 connection...
(based on a Disney timeline I found online:
http://www.islandnet.com/~kpolsson/disnehis/)
-WED Enterprises became Walt Disney Imagineering in January 1986.
-Shareholders voted to change the company name from Walt Disney Productions to The Walt Disney Company on Feb 6, 1986.
Either of those two could conceivably be it. Both names would be 23 years old...
-The Disney Channel aired a 9-part mini series "Return to Treasure Island"... (Though I think the teaser for that would have been "Arrrrrrrr you 23?")
-The Living Seas opened Jan 15, 1986... But it just got a redo, so I doubt it's this.
-The one item that Spaceship Earth enthusiasts haven't realized in all this discussion: the Walter Cronkite version of Spaceship Earth opened on May 29, 1986. Maybe this is the officially un-official opening date of the now-completey-finished SSE descent with its now-23-year-old "Tomorrow's Child" restored?
-Big Thunder Ranch in Disneyland opened June 27, 1986.
-The Mark V trains went into service on the Disneyland monorail sometime in 1986. Maybe this is their send-off?
-Captain EO premiered in September 1986.
-I know "Great Mouse Detective" was mentioned in the thread, but "Flight of the Navigator" was also released that year.
-Rob