True... I tend to use "acceptance testing" for everything that isn't "unit testing", but that's probably not very accurate. Functional testing or system testing is probably a better term. Though Grig pointed me to this: http://atomicobject.com/systir.page (a Ruby test system) which is really an acceptance test (specifying requirements at a fairly low but not obscenely low level), and that could fit into this model. It's not a comprehensive acceptance test, but it isn't too far off. Automated acceptance testing is possible -- FIT is an example of that sort of thing.
Also, by doing this as a script you can avoid sensibility entirely -- you can jump to another page based on any calculation you choose, possibly derived from a regular expression-based parsing or whatever works. You aren't restricted to just following links and filling in forms that you can find on the page.