They're really going out of their way to not use Solaris.
Considering that the Illumos kernel is basically the OpenSolaris kernel, I don't understand what you mean. They are using Solaris, but for some reason they're trying to hide it.
This project is certainly not using Solaris which is now an Oracle product (and trademark) and not open source. It is based on Illumos (which originally came from an OpenSolaris kernel as you said) but my understanding is that OpenSolaris as a project is dead. I don't think it's hiding something to name-check Illumos instead of OpenSolaris.
Illumos != Solaris, unless you'd like Oracle to beat you with a stick for trademark infringement.
I suppose they could refer to it in technical documents as "the OpenSolaris kernel", but by that same logic, an OS using the DragonFly BSD kernel should say it's using "the FreeBSD kernel".
Considering that the Illumos kernel is basically the OpenSolaris kernel, I don't understand what you mean. They are using Solaris, but for some reason they're trying to hide it.