Yep, that's right.
One point which may be relevant is that I first tried this from a website running on my local machine, port 8000. I then tried it on another server running on normal port 80. Both were ip-only hosts - no domain name.
I've tried different browsers, anonymous mode, etc. As I say, the cookie is assigned, and it is persistent on the browser, but a new anonymous Lead ID is created for each request. Each Lead ID has one bit of activity related - a single webpage access.
Any ideas?
Dan