Assuming this is not a case of writers not being up on the script and show specifics (which happened several times during the run of Voyager) the show attempts to set up the possibility of effective communication with several foreshadowing events. It is unfortunately likely the writers/producers did not take previous episode information into sufficient account. Some hand-waving is necessary.
Voyager had already predetermined flight plan at this point. This information was sent with the holographic Doctor two years prior. Voyager had already indicated the path they were going to take and had informed Starfleet. During the briefing with Admiral Paris, we are informed of the estimated path of Voyager. (As seen on the display during the briefing).
The second foreshadowing occurs a few seconds later when the commander continues with,
"As you know we've been working with the Vulcans on the deployment of the Midas Array. Though we are still in the testing phase, we think it won't be long before we can use this technology to send signals at 'hyper-subspace speeds', a message that would normally take years to reach its destination could be received by Voyager in a matter of days."
These regions were already determined and even if Voyager was far beyond those regions, the show sets up the notation of a "hyper sub-space communication channel" which would be far faster than normal subspace communication.
"Assuming they are still on course for Earth, we have established a likely course of trajectories. Estimating an average warp speed of 6.2 and accounting for various astronomical obstacles, we can reasonably assume Voyager is in one of these three sectors."
Even if Voyager were supposedly far from their estimated position, the singularity/wormhole was able to be detected by Seven of Nine in her highly specialized astrometrics setup designed for long-range scanning and the emergency beacon was clearly able to be distinguished and recognized by Voyager's crew.
Was there a degree of luck? Absolutely. But Barkley had also spent a significant amount of time knowing the limitations of both Voyager's technology and the Midas Array and had obviously compensated for the difference in location using the more advanced communication methods.
Was there the possibility of a mistake due to the miscommunication of writers? Very possibly, but the show was made with sufficient wiggle room to allow for some degree of fudging between episodes. It is unfortunate this episode is a lot less accurate than most.