Scheduled tasks running in %systemroot%\system32\

You could run it silently using a Windows Script file instead. The Run Method allows you running a script in invisible mode. Create a .vbs file like this one

Dim WinScriptHost
Set WinScriptHost = CreateObject("WScript.Shell")
WinScriptHost.Run Chr(34) & "C:\Scheduled Jobs\mybat.bat" & Chr(34), 0
Set WinScriptHost = Nothing

and schedule it. The second argument in this example sets the window style. 0 means "hide the window."

Complete syntax of the Run method:

 object.Run(strCommand, [intWindowStyle], [bWaitOnReturn])

Arguments:

• object: WshShell object.
• strCommand: String value indicating the command line you want to run. You must include any parameters you want to pass to the executable file.
• intWindowStyle: Optional. Integer value indicating the appearance of the program's window. Note that not all programs make use of this information.
• bWaitOnReturn: Optional. Boolean value indicating whether the script should wait for the program to finish executing before continuing to the next statement in your script. If set to true, script execution halts until the program finishes, and Run returns any error code returned by the program. If set to false (the default), the Run method returns immediately after starting the program, automatically returning 0 (not to be interpreted as an error code).

0x80070005 is an "E_ACCESSDENIED" error.

The Resultant Set of Policy (RSoP) tool is your friend.

Run an RSoP on an affected computer (Start / MMC / Console / Add-Remove Snap-Ins / Resultant Set of Policy / Add / Close / OK, Right-click the "RSoP node in the left pane and do "Gather RSoP Data...", take defaults) and see if you see any group policy settings applying to the computer.

It sounds like somebody is pushing down a filesystem policy to modify the NTFS permissions on the %SystemRoot%\Tasks folder, but that's just a guess.