This is the official Disney list of "Mainstream Lines" from their website - those lines that are wheelchair accessible and wheelchair/
ECV users wait in line with everyone else.
As you can see from the list,
Space Mountain is listed as a Mainstream Attraction, so why the people you saw came thru a different door, I don't know. But it is listed as one where people with wheelchairs wait in line with everyone else.
Mainstream Attractions
Magic Kingdom® Park
Ariel's Grotto
Astro Orbiter
Buzz Lightyear's Space Ranger Spin
Donald's Boat
Judge's Tent
Mickey's Country House
Mickey's PhilharMagic
Minnie's Country House
Monsters, Inc. Laugh Floor
Pirates of the Caribbean
Space Mountain®
Splash Mountain®
Stitch's Great Escape!
"The Enchanted Tiki Room Under New Management"
The Hall of Presidents
The Magic Carpets of Aladdin
The Many Adventures of Winnie the Pooh
Tomorrowland® Indy Speedway
Toontown Hall of Fame
Walt Disney's Carousel of Progress (seasonal)
Epcot®
FUTURE WORLD
Imagination!: All Attractions
Innoventions East
Innoventions West
Mission: SPACE
Test Track
The Seas with Nemo & Friends: All Attractions
The Land: All Attractions
Universe of Energy: "Ellen's Energy Adventure"
Wonders of Life: All Attractions (seasonal)
WORLD SHOWCASE
China: "Reflections of China"
France: "Impressions de France"
FriendShip Boats
Norway: Maelstrom
The American Adventure: "The American Adventure"
Disney-MGM Studios
Disney-MGM Studios Backlot Tour
Fantasmic!
Lights, Motors, Action! Extreme Stunt Show
Muppet*Vision 3D
Playhouse Disney - Live On Stage!
Rock 'n' Roller Coaster® Starring Aerosmith
Sounds Dangerous - Starring Drew Carey
Star Tours
The Great Movie Ride
The Magic of Disney Animation
"The Twilight Zone Tower of Terror"
*Voyage of the Little Mermaid
Walt Disney: One Man's Dream
Disney's Animal Kingdom® Theme Park
Caravan Stage: "Flights of Wonder"
DINOSAUR
Expedition Everest
Finding Nemo - The Musical
Grandmother Willow's Grove: "Pocahontas and Her forest friends"
It's Tough To Be A Bug
Kali River Rapids
Kilimanjaro Safaris
Lion King Theater: "Festival of the Lion King"
Maharajah Jungle Trek
Primeval Whirl
The Boneyard
TriceraTop Spin
For a very few attractions, there is an alternate entrace because the regular one isn't accessible and was not able to be made accessible (most in MK or Epcot since they were built before accessibility was thought of). There are some others, where the boarding area is not accessible and wheelchair/ECV users wait in the regular or Fastpass line and then are pulled into a different area for loading (Buzz Lightyear, Haunted Mansion and Splash Mountain are examples).
One of the other things that people who don't use wheelchairs don't know is where people with wheelchairs go when they are taken out of the line. They assume those people who 'disappear' from the line are boarding right away, but that is not usually the case.
If they can't board at the regular boarding spot, they are pulled out of the line - usually just before the regular line gets to the boarding area (so they have already waited as long as everyone that got in the line the same time as they did).
For example, at Buzz Lightyear, the 'pull off point' is after you have gone thru the room with the large Buzz Lightyear, near the point where regular line is beginning to enter the actual boarding area with the moving walkway. Guests with wheelchairs/
ECVs are pulled out of line at that point and sent to the exit - not to board right away, but to wait.
At Buzz, we wait in a hallway between the boarding and exit areas until a CM comes to get us - which usually takes 3-5 minutes (remember, we got out of the regular line just as the other guests ahead of us got to the moving walkway to board).If there are too many people with disabilities already on the attraction, you have to wait for some to get off (for fire safetly and evacuation reasons), so the wait may be even longer.
Because our DD can't get out of her wheelchair easily, we have to wait extra for a special car that the wheelchair can be loaded on. If it just wentby when we tell the CM we need it, we have to wait for one whole ride cycle for it to come back around.
By the time we get on, the people who were right ahead of us in line have been off, looked at their pictures and are on their way to the next attraction.
In some rides, boarding at the accessible area means you miss part of the attraction; for example, at Haunted Mansion, you miss the entire 'stretching room' part of the attraction.
The Safari at AK is notorious for extra waits for people with disabilities. Our longest wait there was an EXTRA 40 minutes at a time when the regular line was walk on and Safari Trams were pulling out partially loaded because people were not walking up fast enough to fill them.
Spaceship Earth is currently being renovated, but is a ride with a handicapped entrance. During times when other passengers are able to walk right on (late afternoon is usually a 5 minute or less wait), our wait is usually 20-30 minutes.
For the buses, there are only 2 possible wheelchair spots (if all the equipment is working, which it sometimes is not). It is much harder and takes more time to load a wheelchair on a bus that is already partly filled (plus some people have enough trouble manouvering into the spot when no one is on the bus). Disney generally 'counts' a wheelchair party as a total of 6, five plus the person using the wheelchair or ECV (that is both for the bus and for rides/attractions).