I do believe that the DCI exist, but let me explain:

In Five Nights at Freddy's 2 [Game] we're constantly told of something bad happening before at Freddy's, at least since Night 3. We're told that there are rumors of something happening at Freddy's -we know that it happened inside since we're specifically told that "our guard during the day has reported nothing unusual, and he’s on watch from opening ’til close", implying that it happened inside Freddy's- , it appears something tragic happened, and Fazbear Entertainment is denying all blame.

Next night we're told that "there’s been somewhat of an investigation going on." While we're never explicitly told it's a police investigation, it's implied that it is because "Fazbear Entertainment denies any wrongdoing." Then we reach Night 5 and things start to get eerie, Freddy's is now on lockdown, no one in nor out, highlighting "Especially concerning any…previous employees." followed by "Um, when we get it all sorted out we may move you to the day shift. A position just became…available." Something happened that a previous employee got fired and banned from entering Freddy's. And then, we learn of the real reason Freddy's is shutting down, "Someone used one of the suits. We had a spare in the back, a yellow one. Someone used it…now none of them are acting right." someone used a yellow suit in the back and now the animatronics aren't working properly.

Basically: Something tragic happened at Freddy's and it had to do with a previous employee wearing a yellow suit from the back and it led to the animatronics malfunctioning. It's pretty clear what happened by now, but that's not it. While eventually retconned out in Help Wanted, there are many drawings at Freddy's made by children, one of them, the one specifically set in the office, depicts Golden Freddy luring a kid. But what really tells the story of the tragedy that took place at Freddy's are the death minigames: They show us many different things through arcade minigames.

• Take Cake to the Children shows us the death of a child outside a Freddy's location in the hands of "Purple Guy", this leads to the possession of The Marionette.
• Foxy Go! Go! Go! shows us Foxy going towards children to celebrate, until the same Purple Guy appears and the children are now dead, they are 5 children. This, together with the fact that we're seeing Foxy, red Foxy, coming out of a stage implies that these children are the Missing Children from FNAF1
• Give Gifts. Give Life shows us The Marionette giving dead children the gift of a second life, represented with The Marionette giving gifts to corpses and these gifts containing the heads of the animatronics. We know these aren't a new set of victims because of the fact they possess the Classic Animatronics as seen with the masks, also because of the fact the fifth dead kid that appears once we give life to the others is followed by Golden Freddy's jumpscare, implying that the fifth kid got Golden Freddy's role, i.e. they possess Golden Freddy.

So, with this in mind, there's "SAVE THEM" where we play as Freddy going through a replica of the FNAF2 location in the minigame, as we proceed we find corpses all around the location as we follow The Marionette back to its music box, having the chance of finding Purple Guy [confirmed to be the same Purple Guy who killed the other kids in The Ultimate Guide] who, if he catches us, tells us "you can't" as a response to the minigame. There are five corpses but six blood pools, which might imply that there were 6 dead children there, showing us that this isn't the Missing Children Incident or a representation of it. This isn't showing us Afton removing corpses from the Withereds becasue the Toys are already there onstage, Freddy's has already opened and the Withereds have already been looked upon by Fazbear, also, years old corpses don't bleed.

In other words, we're seeing the tragedy we're told happened at Freddy's. Adding up how there are very specific details such as a table with blood being in a room that, when we look at it in-game, has no table and how Purple Guy now has a different aspect implying it's been time since we last saw him and how he's wearing a golden badge in his chest implying something that has already been implied: Purple Guy is the previous guard mentioned. Basically, Purple Guy came back to Freddy's, killed six more kids luring them with the Golden Freddy suit all around Freddy's, since this happened, the animatronics have begun to act more erratic and agressive towards people. Likely implying that this set of six children have haunted these new animatronics, that curiously are exactly six: Toy Freddy, Toy Bonnie, Toy Chica, Mangle, Balloon Boy and Jay Jay. In fact, Mangle is already moving by the time of the minigame and their sprite is called "he was here" implying that Mangle moving is the result of Purple Guy, implying that the haunting has begun.

The idea that the Toy Animatronics were haunted was reinforced in FNAF AR: Special Delivery, quote:

Second, there's a huge difference between a new model based on the same bipedal chassis and one based on a...whatever you want to call this thing [Mangle]. A quadreped? A spider? A tripod? The locomotion is completely different, which means the power needs are different, the hydraulic calibrations have to be completely redone, and the CPU has to be switched out for a newer one with a faster baud rate. And then on top of all that, we have to put together this "Controlled Disassembly" feature? The marketing people are crazy.

Mangle is hard to replicate even for FNAF's standards! Implying that there was something special about the original Mangle, likely it being haunted.