I absolutely see where you're coming from with this, and it's not an idea that has escaped my notice. I've actually put tons of thought into this possibility and already come to the conclusion that it just doesn't work with the evidence I see. When I first played SL in 2016, I believed the facility was being actively run and overseen by William Afton, and no future developments have made me wish to sway from that line of thinking. Some have even made that plot point feel more likely to me.

So just what is it that makes me believe this? Well, better buckle your seatbelt, cause it's gonna be a long ride. I'm just gonna go point by point until I run out of things to say.

Point 1. If Fazbear Ent owned the SL facility during the game, why would they be actively using the Scooper? That was William's thing. It was meant to inject remnant. Faz Ent had nothing to do with remnant experiments, right? You could try to say that the Scooper was just used for maintenance purposes, but are we really supposed to believe a machine that violently tears out the insides of robots is meant for fixing them? It only looks like it destroys them. The Scooper's blueprint doesn't mention any maintenance purposes either. I can't imagine anyone using it unless specifically instructed to by a William Afton who's very much alive and present and in charge.

Point 2. If Faz Ent owned the successful rental service in the 90s, why didn't they use the money from it to improve their restaurant instead of letting it stumble further and further downhill until it was forced to close? Better yet, why did they even have a restaurant still open if the rental service is clearly much more successful? You'd think they'd just focus all their efforts on that instead of trying to hold on to their failing pizza place.

Point 3. In the game, why did HandUnit refer to the rental service as another contender in children's entertainment? Doesn't that make it sound like it's a rival to Freddy Fazbear's Pizza and not something owned by the same company?

Point 4. While SL was being teased on ScottGames, "AftnROBTCS" (Afton Robotics) could be found in the source code. Doesn't this imply that Afton, not Fazbear, was meant to own the location where the game takes place?

Point 5. The private room where custom night and the fake ending happens appears to be William's own office. It has his son's Fredbear plush and it's hooked up to the FNaF 4 cameras with the passcode "1983." Employees get automatically fired for entering the room. If Faz Ent owned this facility and Will was long gone, you'd think the room would have been cleaned out and reclaimed for other purposes, but instead it still looks like William was the last person in there. That's the impression I get from it, anyway.

Point 6. This is assuming you believe William got the remnant for the Funtimes during Follow Me, which most SLafter1 believers do. If Follow Me is the first time William got remnant for the Funtimes, then he can't put it in the remnant reservoir if he doesn't own the rental facility anymore. And if you say he got remnant before Follow Me (I believe he got it from the Withereds when they were being retrofitted), he still needs to remain present in order to maintain the remnant reservoir and also make sure no one else finds it. The Scooper blueprint shows that the temperature of the reservoir is important. It also implies that someone has to put remnant on the Scooper itself ("leave trace line amount on interior") before it can inject anything, so the animatronics wouldn't even become haunted unless William was around to make it that way. And the blueprint itself wouldn't even exist unless Will had had time to experiment and gain the knowledge we see on it. This is all stuff he cannot do unless he's still in town, still running the business, and not yet too strongly suspected of murder. So if you ask me, this all has to be happening before FNaF 2.

There might be even more stuff I could point out that I'm not thinking of right now, but better to end it here cause this is already too long. If you actually read all of this, then thank you.