You are very much correct. I read the reddit post and apparently Sean said that when you get close enough to another player you will connect to their "private server". If this is how it works and the servers were having issues, then nobody would've been able to connect to someone else's server, meaning they wouldn't be able to see each other, which also explains why the time of day was different. When base building comes out we will be able to see if it actually is multiplayer because we will be able to see if we see what other players see. We might even be able to see if multiplayer is a thing when PC comes out because it'll be easier to communicate across steam and you can data mine to see if there even is a player model.