With all due respect, the culprit behind this issue is already known, and has nothing to do with Location Services.
The issue is that iTunes is storing a cookie in Safari's (or should I say, WebKit's) respository in ~/Library/Cookies, and balking when the cookie doesn't exist (such as when Safari is reset) or has the wrong value.
Now, iTunes could easily store this marker in another location, as it already does for the machine's authorization key, but it doesn't, and it also ignores its own preference to disable Automatic Downloads, and asks for the password anyway, no matter the setting.
It's easily, and completely reproducable by manipulating the Cookies.plist file.
Log in to your iTunes account a few times, or make a few purchases, to reach some as yet undetermined threshhold (I'm too lazy to try), and the nagging dialog goes away.
With such a state settled, quit iTunes, and temporarily move the Cookies.plist file to the desktop or another location.
Launch iTunes, and get nagged. Twice.
Quit iTunes, then restore the temporarily displaced Cookies.plist file to its rightful home, overwriting the newly generated file. (Note that that file only contains a single cookie for the apple.com domain.)
Launch iTunes. No nagging. No problem.
IMO, and Apple obviously disagrees, that it's poor form to have one application affect another's applications settings, or behavior.
Fine, if they want to keep all the cookies in a monolithic file, since the iTMS is, afterall, really a highly-customized website that the iTunes app relies on the WebKit framework to render.
However, the question then becomes why iTunes still prompts for the password for a feature that the user has explicitly disabled? This makes no sense, on either a logical, or technical level, and is the root flaw that should easily be correctable.
For various reasons, many users choose not to be logged into their iTunes accounts, and are asked to enter their passwords only when performing a transaction, or a task that involves sensitive information.
Why then, another standard when it comes to Automatic Downloads? And for every user, whether the feature is enabled or not?
It is clearly an inconsistent, and flawed behavior, that Apple apparently chooses to ignore.