This is way too trivial. HTTP is based on TCP (more exactly, this is a
dominant protocol); and a server socket always knows the client's IP and can do with this information whatever required. If you do your HTTP request, it may or may not come to the server from your client of your host with you computer's IP directly, more typically, some middleman agent does it on your behalf. Even if your computer's IP address can be dynamic, and most usually it is.
So, your admin is right, listen to this person to learn what sits in the middle of you and the HTTP server use connect to.
At the same time, it does not mean the server cannot spy on you at all. If you connect from your company; and the company use static IP address for outside word, the spy knows where do you work, can collect statistics of your connections, and a lot more. So, firewalls, etc., provide considerable protection but does not provide truly anonymous connection.
If you want to learn about "anonymous communication" you may want Google for these words. In particular, read this:
http://en.wikipedia.org/wiki/Onion_routing[
^]
Don't mix it up with secure connection (
http://en.wikipedia.org/wiki/Secure_connection[
^]) via
secure protocol such as HTTPS, where your data sent via network is ciphered, but it does not mean your identity is hidden.
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