My guess is that this behavior is caused by PowerShell's concept of session state which is documented a little bit on MSDN. The reason you're seeing different behavior with HotkeyNet's "Run" and "run as" syntax is because HotkeyNet uses the OS's CreateProcess API in the first case and CreateProcessWithLogonW in the second case. (This is documented on HotkeyNet's website.) If you look up those APIs on MSDN, you'll see that in the first case, PowerShell runs in HotkeyNet's security context but in the second case, it runs in the account's security context. My guess is, in the first case, the OS starts a new session state from scratch, but in the second case, where your account credentials are used, PowerShell uses a global state belonging to the account.

You may be able to avoid the whole problem by starting PowerShell with HotkeyNet's "Open" command because it uses the OS's ShellExecute API.