Proprietary drivers can interact with the Linux kernel.
Provided they only use fairly generic OS-functions, which are to be found in many similar kernels. Such drivers, which do not rely on Linux-specific functions, cannot be considered "derived works" of the Linux kernel, and are therefore free to choose whatever license they like.
However, any driver which makes use of Linux-kernel-specific interfaces, which are not found in other OSs (even in other Unix-like kernels) are, pretty much by definition, a "work based on the program" of the kernel and therefore must be licensed similarly. See the text of the GPL-2, which the kernel is licensed under:
https://www.gnu.org/licenses/old-licenses/gpl-2.0.html
> This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law:
> These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it.
Note that the LGPL exists specifically to allow the linking of separate Free and proprietary software, which is forbidden by the GPL. But Linux is licensed under the GPL-2, so those extra permissions do not apply.
If the Nvidia driver stuck to the generic kernel API, it would be fine. But it doesn't. It tries to use Linux-only APIs, which are marked for use by license-compatible GPLd drivers, without itself being GPLd.
This is a clear violation of the Free Software license that Linux is made available under.