I'd assume they were assuming a worst case scenario of something like a ballast malfunction paired with a propulsion malfunction, so you have a partially buoyant (enough to stay off the ground, not enough to surface) craft being pushed both by currents, and possibly its own propulsion, in an unknown direction in some radius outside of the Titanic. I've no idea of the depth sonar can accurately ping, so they may also have been considering the 3-d area around the Titanic in which case you're hitting radius cubed, and so even a "small" max distance could be huge.
The Navy & Coast Guard would definitely have access to their own fleets
This sounds a lot like https://xkcd.com/793/ - "and then add some secondary terms to account for <complications I just thought of>."
They lost contact 105 minutes into a 120 minute, 2.5 mile descent. The release point for that descent was well known, and currents estimated closely enough to allow the sub to descend close enough to the shipwreck that the submersible's thrusters could move it very slowly to viewing locations.
They don't know what happened to cause it to lose contact more than a quarter mile above the ocean floor. They didn't know whether it went neutrally buoyant at that point, whether it ascended quickly, or slowly, or stayed near the bottom of the ocean and continued looking at the Titanic and only later drifted off course - they've done that before. Those ocean currents, unknowns, and distances are large; merely pulling the release point from a GPS track does not suddenly make the search point tiny.
Modelling and knowing surface currents is one thing, but this submersible was thousands of meters deep. Deep ocean currents can be very fast, change often, and we have way less data on them.
- Oceangate, probably
I can think of 10 different ways to maintain some contact with the surface and store some data about dive conditions. Honestly perplexed at all the people who are still buying into Oceangate's demonstrably bad way of doing things and just saying it's impossible to do any better.
drop a penny into a swimming pool vs drop it into the ocean.
This was the size of the search _on the surface_.
I keep seeing reports that they've search an area "the size of" Massachusetts or Connecticut. Shouldn't OceanGate have recorded the exact coordinates where it was released and then been able to localize its possible location to a small area around that by modeling ocean currents or something? My understanding the Titan was designed to sink to the bottom and could only move very slowly under its own power. I know OceanGate was cocky and cut a lot of corners, but I just can't believe they wouldn't have the exact release location recorded somewhere, even if it was just an automatic track log on their ship's GPS navigation system.