I get the impression here that piwik has a JS (or other) link in each published page rather than logs being aggregated through the server, which is the default/usual state for web sites. Is that correct?
That's the only way I can see a log analyser issuing its own cookies.
In Firefox I have set "I do not want to be tracked. In theory that would be interpreted by a site as "I will neither set any cookie nor track your progress through this or any other web site". I very much doubt this is what happens: cookies, I know, are set on my machine to tell web sites that they should not track me. I have no idea whether they honor this or whether they use the no-track cookies to track me. Whichever, the ideal intent is not being honoured, I'm sure of that.
I agree that most humans - and certainly any bureaucrat - have no idea how the simplest internet protocol works and almost certainly, when presented with a "this site sets cookies" warning, simply click in frustration rather than find out what it does.
I have no warnings on my sites other than in "site FAQs" - but then, I only set temp session cookies. Which EU now say is ok, despite panicking us before.