First, the Nikon post (which only shows on the 3.11 firmware pages):
An issue has been identified in firmware versions 3.10 and 3.11 in which fine-tuning values selected for AF fine-tune > Saved value are not correctly applied when pictures are taken. A fix will be made available via the Download Center as it becomes available. We apologize for any inconvenience this may cause.
Next, Nikon Rumors' headline: "Do not install the latest Nikon Z5/Z6/Z7 firmware update."
Unfortunately, both these things are problematic. First, Nikon's warning doesn't appear on the 3.10 update pages (nor does it appear on the Z5 update page). Keeping a Web site accurate and up to date with so many moving parts is hard. I know, because I struggle with it every day. But Nikon really needs to elevate their warning so that everyone know what's happening, and that there are consequences if they've already updated their cameras. And the warning needs to appear on all the pages for which the problem is active.
However, Nikon Rumors is overstating the problem, and there's a secondary consequence of not making the update: you can't use the new teleconverters, nor can you update lens firmware with an F-mount lens in the FTZ (though this currently only impacts one lens that I know of). Moreover, there were bug fixes in 3.10 that some people actually would want.
There's no need to panic here. First, AF fine-tuning options isn't something you'd tend to do with Z-mount lenses. I've not encountered a native Z lens to which I'd want to make an adjustment. If you're making AF fine-tuning options with a Z-mount lens you probably instead need to check to see if that lens has focus shift and learn how you deal with that.
I have seen F-mount lenses in the FTZ adapter that need AF-Fine tuning, though generally not any recent Nikkor. So, yes, there are some folk that would have to turn off Saved Value in AF-Fine tuning options and live with a not-optimized system if they've already updated their firmware, or who need to update their firmware to take advantage of one of the other things those updates enabled.
Note to Nikon: this would be a good time to "fix" your naming ;~). On most Z cameras, the menu item is AF fine-tune, while on the Z5 it is AF fine-tuning options. I believe that the latter is Nikon's current templating.
