It looks like you are part of the project. Can you clarify what you mean by "license-free"?
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.
My view is that all these, ah, parameters for licensing - what is or is not, copyright, public domain existing in some countries and not others, etc, etc - none of these are things I have chosen. They are being imposed upon me. This is not okay. I feel no need to go along with it all, just because other entities force it upon me.
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."
Legally "all rights reserved" is the default, until/unless you follow the legally appropriate ceremony to disable it. If you get the ceremony wrong in some way then you're back to "all rights reserved" in practice, regardless of intent.
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.
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.