The "or very definite answers to the question" is important there. Linus has explicitly answered the question, and if you use any of the Linux headers then yes you should release that software under the GPL. Under this circumstance your "which is definitely not the case" is incorrect.
[EDIT: after reading the information in the link provided by actionfromafar, I'm pull that back a bit: headers marked appropriately can be used and provided a shield similar to scales via glibc & similar (see below) - but check any headers you do use to make sure that they are in fact thusly marked (and note that this goes back to my "… or very definitely answers the question")]
It has also explicitly been said that making calls to the kernel indirectly by other means does not carry the same requirement, so if you use glibc (to give what is perhaps the most common example) and it causes the kernel to be called, you do not inherit GPL requirements from the kernel. What requirements you inherit depend on the license of the library, in this example LGPL which is glibc's license and that doesn't confer any such requirement from linking or other such coupling.
Whether this indirect call via another library that isn't itself GPL licensed acting as a shield holds generally, or just where explicitly stated as with Linux, I'm not sure off the top of my head. I'd have to reread the licence to refresh myself on the exact details and that isn't something I have the time to do right now, but in the case of Linux it doesn't matter if that is a general property or not because of specific things that have been officially stated.
There is a further exception that allows the making of binary blobs to act as drivers and such writing the kernel. I'm not sure if that is just a refinement of the same shield, or something more specific. Again I'd had to reread to be more sure (I've not gone over the "fine print" here in detail for some years).
> Using background service such as Minio as an unmodified black box for data storage as part of your app is unambiguously not derivative work.
That is certainly the case for LGPL, but by my understanding it isn't for GPL nor by extension AGPL. Minio's maintainers themselves shrug on the matter and suggest you either lawyer up or pay for commercial licensing if your work is not also AGPL and therefore directly compatible (see https://github.com/minio/minio/blob/master/COMPLIANCE.md).
Nope. That is LGPL. Under (A)GPL if you make a derivative work you have obligations even if you do not modify. Easy.
[Well, not so easy, as this discussion and the likes of Minio saying “get your own lawyer to tell you what our licence says” illustrate – what constitutes a derived work is apparently not objectively well-defined]
[EDIT: after reading the information in the link provided by actionfromafar, I'm pull that back a bit: headers marked appropriately can be used and provided a shield similar to scales via glibc & similar (see below) - but check any headers you do use to make sure that they are in fact thusly marked (and note that this goes back to my "… or very definitely answers the question")]
It has also explicitly been said that making calls to the kernel indirectly by other means does not carry the same requirement, so if you use glibc (to give what is perhaps the most common example) and it causes the kernel to be called, you do not inherit GPL requirements from the kernel. What requirements you inherit depend on the license of the library, in this example LGPL which is glibc's license and that doesn't confer any such requirement from linking or other such coupling.
Whether this indirect call via another library that isn't itself GPL licensed acting as a shield holds generally, or just where explicitly stated as with Linux, I'm not sure off the top of my head. I'd have to reread the licence to refresh myself on the exact details and that isn't something I have the time to do right now, but in the case of Linux it doesn't matter if that is a general property or not because of specific things that have been officially stated.
There is a further exception that allows the making of binary blobs to act as drivers and such writing the kernel. I'm not sure if that is just a refinement of the same shield, or something more specific. Again I'd had to reread to be more sure (I've not gone over the "fine print" here in detail for some years).
> Using background service such as Minio as an unmodified black box for data storage as part of your app is unambiguously not derivative work.
That is certainly the case for LGPL, but by my understanding it isn't for GPL nor by extension AGPL. Minio's maintainers themselves shrug on the matter and suggest you either lawyer up or pay for commercial licensing if your work is not also AGPL and therefore directly compatible (see https://github.com/minio/minio/blob/master/COMPLIANCE.md).