NSIS Access Control problem with built-in users group

I was dealing with a subtle issue recently involving setting access permissions using NSIS (Nullsoft Scriptable Install System). In the end, it turned out that the problem was not with NSIS at all. Rather, it was a misunderstanding on our part regarding an unexpected quirk in Windows. However, hopefully this post will help anybody who encounters a similar issue.

Our installer was supposed to enable read/write permissions for all users on certain important files and registry keys. However, some users were finding these files/keys were not accessible, and it was preventing the software from working correctly.

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