That was also my understanding of the GPL, but the AGPL is for me to understand.
You wouldn't, as system interfaces are specifically excluded as an AGPL enforcement domain. But if the Linux kernel was AGPL, you would have to supply the source code to your NFS clients, since those clients would be served directly by the kernel.
More specifically, the only difference between GPL and AGPL is section 13 (and the preamble summary). The rest of the license is word-for-word identical (save for the name). https://www.gnu.org/licenses/agpl-3.0.en.html#section13