Unless and until I see a clear privacy police analyzed by a lawyer, stating categorically that this doesn't happen, I think it's wise to assume that you are correct here.
While it's possible they meant something nefarious, I think the goal was probably just to prevent confusion around shared computers. Such confusion might seem unlikely, but when your market is as big as Microsoft's even unlikely things happen all the time.
Microsoft's "CoPilot PCs" scheme places a lot of emphasis on the hardware being powerful enough for locally-processed "AI" features and isn't about offloading everything (I suspect because they're starting to acknowledge that not everyone has a highly-reliable multi-megabit Internet connection).