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VERY NICE

The reason you're experiencing user authentication errors is because you're running the script against the developer test url:
https://apitest.authorize.net/xml/v1/request.api
while using your real authorize.net login id and transaction key.

By "real", I mean the credentials you'd actually use in a live, business environment. Those credentials will only work with the production url:
https://api.authorize.net/xml/v1/request.api

The developer test url is only for those who registered for a free authorize.net developer test account. Your real, live authorize.net account login id and transaction key won't work with the 'apitest.authorize.net' url.

It's silly that Authorize.Net doesn't allow developers to perform 'test' requests against the 'production' url. It's funny that their developers weren't able to tell you the reason why your requests were being rejected. Maybe it was just too obvious.

So you have two ways to deal with this:

1) Register for a authorize.net developer account to get a login id and transaction key to use against the "test" url. Click the "Request a test account" link near the bottom of this page:
http://developer.authorize.net/

2) Just use the existing developer login id and transaction key that's already included with the script. Yes, they are real and do work.