If the Kobayashi Maru was skirting the Neutral Zone at the time of the accident, a ship with a busted navigation system could easily drift a few million kilometers off course--and cross well into the Neutral Zone, IMO.
Makes sense in this special case: we know that skirting that close to the RNZ does win a significant amount of time on a Gamma Hydra / SB 10 run at least, so civilian UFP ships might well be interested in shaving off a few days from their schedule. Granted that Gamma Hydra didn't seem to be any sort of a commerce hub, but there could still be major traffic in the region if it warrants a full starbase.
Of course, one wonders how the Zone is marked in the first place. We've never heard of marker buoys, so probably the treaty specified a Zone border in relation to some "fixed" points such as stars. Yet stars do drift, and the Feds and the Romulans might have differing ideas on how that affects the exact placement of the Zone. Say, the Zone might be fixed in terms of "epochs", so that while the fixpoints drift constantly (and perhaps unpredictably), the Zone only moves (or is redefined in terms of the fixes, even if the idea is that it stays in place) every fifty years or so. And Romulans might quote obscure complications in the epoch system when it suits them - plus they'd be within their rights to mine their side of the Zone, after which the Zone might move but the mines would stay in place and eventually endanger UFP shipping!
But in regards to there being no Klingon Neutral Zone, there was a female admiral...
Yup. Doesn't necessarily mean the KNZ existed back in the early 2280s already, though. Could have been something they dreamed up during the putative détente brought by Kirk and Korrd's meeting in ST5, for example.
I'd sort of prefer to think that the Zone in ST2 was the Romulan one, because that one was explicitly associated with Gamma Hydra in TOS. That there'd be Klingons there would be plausible if there was a Romulan-Klingon alliance in existence (and TOS and TNG at least allow for this if they don't quite confirm it) - and such an alliance might already be history by the time Saavik takes her test, but the scenario might still be played out because it's a historically interesting one.
If we assume the scenario has any historical basis, we might just as well note that it's already being used in that exact form in 2258 in STXI. And the novels currently have the scenario being loosely based on something Archer did in the mid-2150s...
Timo Saloniemi