This statement is positively false when it comes to running an adventure as part of an Organized Play program such as
Adventurers League. You cannot for example do any of the following things in AL:
- Add/Delete Encounters
- Increase XP, Treasure, or Item awards
- Use Milestone XP
- Introduce House Ruled creatures, items, rules, classes, races, etc
- Disallow any legal race/class
- Swap creatures in an Encounter (you can add/remove creatures of the same type, but substituting different creatures is not allowed)
- Add terrain, or other encounter features
- Change NPC motivations or allegiences beyond what is stated in the adventure
This is by no means an exhaustive list, but compared to other OP campaigns - AL allows a lot of DM flexibility.