[ghaff]

That's pretty much how I read it as well. Sure, for an internship, lots of enthusiasm probably differentiates you from a form letter and a resume (which, lacking much real experience, doesn't tell you a lot anyway). And, honestly, a followup along the lines of "Thanks. I'm still really interested in your company. Do you have internships or other programs?" would probably have worked at least as well as offering to fetch coffee.

But, as you say, you're probably not going to get an opening created for you unless you have connections and/or a special skillset.