This is why I say license-free. It is rejection of these imposed parameters. I know what I want here - for other people to be able to use the library as they wish for whatever they wish, simple as that. No charges, no catches, go use it.
However, in practise, companies and individuals must abide by all this stuff, and so you see about the code being in the public domain, a license of your choice being granted if you wish for one, etc. This is to address the practical problems involved.
Regarding public domain, I think you've overlooked where it is explicitly placed in the public domain - it's the end of a couple of sentences, so it's understandable;
"If however for legal reasons a licence is required, the license of your choice will be granted, and license is hereby granted up front for a range of popular licenses : the MIT license, the BSD license, the Apache license, the GPL and LPGL (all versions thereof) and the Creative Commons licenses (all of them). Additionally, everything is also placed in the public domain."
CC0 contains the lawyer-developed appropriate ceremony to do what you want here, including handling weird jurisdictions. The way you've phrased it will confuse the lawyers and may or may not "work" legally speaking.
There are instructions on the CC site about how to apply CC0 to a project. CC0 was developed for precisely this purpose.
"Licensing with attitude!"
If there literally is "no license" and something isn't public domain, then it means you aren't authorized to use it (because the authors have a copyright, even if they have thus far chosen not to assert it). And in order to be public domain, it must be explicitly put there. That may be the case, but your page would be clearer if you said so.
And if not, then a license must exist, and you should elaborate it.