Having the program running is enough to be detected by the anti-cheat system. If the Anti-cheat system detects a program running at the same time that Destiny 2 is running, and that program has been identified as a threat, then it will generate an auto-report of said threat and send the data to the team. The team reviews the report and then acts on it. You're in the right location to get support, but, sadly, the support you're after won't be coming. Bungie doesn't discuss restrictions or bans, and as you've determined the very real and possible reason for your ban, and that very real and possible reason is a standard reason that leads to the bans, then it's most assuredly not a mistaken ban. Your computer and the programs running on it is your responsibility. Anti-cheat detection systems are a standard in multiplayer games, and there's plenty of warnings available both on and off of Bungie's website (and not just for Bungie games but many others) that having such programs running during an anti-cheat scan is a bad idea. Sadly, your only option at this point is to create a new Blizzard Battle.net ID and purchase Destiny 2 on it should you wish to continue playing Destiny 2. Blizzard will not issue you a refund and Bungie will not overturn your ban, nor will they even discuss the possibility or explain to you exactly why you were banned. It's policy.