nowhere in the episode they say they are in the same exact spot. They are probably in the same area, as they have been tracking the valiant’s transmitter, but likely not in the same spot.
Area, spot, the same thing. If we imagine the Milky Way to be a disk 100,000 ly across, there are 314,159 lightyears of rim to choose from. If Kirk can scan a generous fifteen lightyears to one side (which is par for the course for 24th century ships), then the odds of him being where he is are a bit below 1:10,000.
Something very specific must have guided Kirk to where the
Valiant's recorder marker noises could be heard.
Also, Delta Vega is obviously quite close to the barrier, so it makes sense for two ships to get there by passing the nearest habitable planet.
Now this is more like it. But if there's an outpost there, it again becomes impossible for the
Valiant feat to be "Impossible!".
If we draw a cone from Earth to the rim of our imaginary Milky Way disk, to mark an approximate beeline to the nearest part of the rim, the cone is still likely to be a thousand lightyears wide at the rim, touching upon dozens of habitable planets; odds of two skippers steering towards the same one are again low, but no longer quite 1:10,000. However, the story doesn't allow for the
Valiant to actually steer.
At the beginning of the episode, Kirk dictates a log where he indicates he knows everything about the
Valiant - save for the fact of how she ended up where Kirk now is. So the one thing explicitly ruled out is that the
Valiant would have been on a mission to the Galactic Barrier! We must begin from the assumption that outside forces led the old ship to this location. Since Spock only gets bits and pieces out of the logs, there's room for speculation.
1) The magnetic storm was a magic carpet ride from a near-Earth location to this very spot, explaining how the old ship could get that far, but also why she would end up here in particular, against her will. But Kirk didn't ride any storms on his way there, so him ending up on the same spot is unexplained.
2) What the ignorant skipper of the
Valiant considered a magnetic storm is merely a regular warp highway, and Kirk indeed used that to get to this particular spot. But Kirk makes no reference to riding a warp highway, either - and if riding one were trivial and expected, Kirk again should not be allowed to be amazed by the
Valiant doing the same.
3) An outside force of some other sort led the ship here. We hear of no hijacking of the outbound
Valiant or
Enterprise - but on the inbound leg, there were demigods aboard on both. Perhaps the ones aboard the
Valiant selected this particular spot for the return through the barrier, possibly because they knew the
Enterprise would be there 200 years later (omniscience is a plausible ability for them, even though not explicated) and intended to benefit from that somehow?
4) There is something really, really interesting about this spot, even though it goes unmentioned in favor of all the surprises. What could it be? Delta Vega isn't it - that place pops up as a mere afterthought. But we can postulate a local landmark that would have lured in both an intrepid explorer like Kirk and a distressed castaway like the
Valiant's Tarasco. Possibly there's a local weak spot in the barrier there (perhaps manifesting as this purple haze, thus explaining why Kirk steers into that rather than past it)?
What our two sets of characters would know about that barrier is unestablished. The events allow for us to think that Kirk expected to find it right there, or that Kirk was surprised by its existence. The dialogue rather favors the former interpretation, though, since we get zero expressions of surprise; thus, Kirk might indeed have been told by Starfleet that the Barrier has a Hole at this specific location, as observed from afar.
Timo Saloniemi