Earlier quoted context omitted.
The question isn't about modifications to the library/service itself, but whether with other code linking to it in any way is what you have considered a derivative work that should also be covered by the AGPL. For a library I'd say that was a definite yes. For a service it is someone's less clear, some provide connective tissue (language bindings or other access modules) under less strict licenses which creates an ob…
The "any coupling" logic would also make anything running on Linux GPL, which is definitely not the case. Using background service such as Minio as an unmodified black box for data storage as part of your app is unambiguously not derivative work. If you were to write something like a management UI for Minio and offer it with your hosted Minio service, then I can at least see the argument, although it still doesn't co…
[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).