How is this different from any other cave/overhead environment?
I'm not sure if you're asking for specifics about this cave, or if you expect one cave to be fairly similar to the next in terms of challenge but caves have quite a wide range of characteristics. I'm not a cave diver and I don't know much about this particular cave beyond what's been reported in this thread, but I do have over 40 years of experience as a dry caver. Figuring that most people don't know much about them I'll offer a bit of information about caves in general.
Those who are familiar with caves only from touring a commercial cave or seeing pictures of the caves in Florida or the Yucatan may tend to think of caves as being relatively spacious, and having water that remains crystal clear unless a diver stirs up the silt. The reality is that caves have a vast range of sizes, from huge rooms and enormous passage to constrictions or entire passages that an average sized person can't fit through. Big or small, those passages often have irregular shapes, so that the available space isn't as big as nominal dimensions suggest. Just because a passage has nominal dimensions of 3 by 4' doesn't mean you'll actually fit through it. The nature of a particular cave is largely a result of the local geology. In some places there are many extensive caves that have large passages, and in others all of the caves are relatively short, with small passages. New Mexico has some very large stuff, such as Carlsbad Caverns, but Santa Rosa is almost 200 miles away and may have very different geology.
Filling a cave with water obviously makes it more challenging to explore, but it's still far easier to explore some of the mostly large caves in Florida and the Yucatan than small caves. When you're exploring a cave rather than just going on a sightseeing trip it can be even more challenging, since you've got much more reason to try and continue despite obstacles that would stop most people. John alludes to this in his post. Nobody has the skill to swim through a really tight passage without stirring up whatever silt is there, and (parts of) the passage may physically impede movement through the passage. Here in the northeast it's common for cave divers to use the rule of sixths instead of thirds since small passages with lousy viz are common. The diving they're doing is almost entirely for the purpose of finding out where the cave goes, and hoping that they'll find more air-filled passage; it's not something that many people would consider a form of recreation.
Here's a brief list of various difficulties you may encounter. Tight bends that can only be negotiated in one orientation, because your knees only bend one way. Tight bends that are difficult or painful in any orientation, and impossible for those with longer legs. Places where your back drags against one side while your chest drags against the other side of the passage. Body-tight constrictions you can only get through facing L, R, up or down. Scalloped walls (from water flow) that act like ratchets, making it far more difficult to go in one direction than the other. Passages that are a bit bigger than your body, but have a narrow fissure in the floor that will happily trap you if you don't hold yourself above it (clear advantage to neutral buoyancy for that). Passages that are easily big enough for crawling (hands & knees or on your belly) but go on for hundreds of yards. There's one in Mammoth Cave (Kentucky) that goes for 7000' without a place to stand up. My personal record is about 1600' before being able to stand up. That same caves has a passage that's 50' tall, straight as an arrow for 2000', and mostly narrow enough that you squeeze through sideways.
During a rescue I made two trips into a particularly difficult NY cave, where it took an hour to get 250' from the entrance to our patient because most of the route was either low enough or narrow enough that you barely fit. At 5'10" and 160 pounds I was one of the largest people who could fit. It sounds like the section of Santa Rosa where this incident happened was somewhat similar to that cave, plus filled with opaque water.
I have no idea how the cave they found was described so differently 40 years ago
People who aren't really cavers often tell amazing stories about caves they've gone into that don't match the reality experienced by real cavers. There's a modest cave that's about 700' long a couple of miles from my house. It's been very thoroughly explored by numerous cavers over the years, and what extremely small chance there is of finding unexplored cave would require digging out glacial sediment. Despite that apparent reality I've met somebody who claims his brother went in years ago and "walked for hours", and another guy who said it "went all the way back to City Hall", which is about a mile away. Another cave a bit further away is 1.6 miles long, but has a N/S extent of about 800'. I've encountered multiple people who believe it's the same cave as a separate one almost 2 miles south. Some are probably just assuming, but I've heard multiple claims of somebody going in the entrance of one and coming out the other. Cavers hear stories of that sort fairly frequently. Overestimating distance is also very common, such as looking down a 15' pit and thinking it's 30 to 50' deep, although it does seem a bit less likely from a rescue diver who claims he couldn't even see the other side.
I assume there was some collapse in the cave passage at one time.
Caves are usually fairly stable, and a good rule of thumb is that if a rock falls on you it's probably because you or somebody in your group dislodged it. Of course such rules always have exceptions, and some caves aren't very stable at all. Caves are formed by flowing water (there are other mechanisms too), so it's normal for a cave that still has flowing water in it to change over time. Obviously that will happen over geologic time periods, but it can happen in very short periods of time, too. Flooding in particular can result in rapid changes. I discovered a room in New York's Knox Cave in 1995, and on a return trip in 2000 another caver and I discovered a second room and some stream passage. We're fairly certain that the connection between the two rooms was (re)opened as a result of flooding sometime between the two trips.
passages that had reportedly been seen 40 years before. (They don't exist.)
Despite what I said above about people commonly reporting things that don't exist I wouldn't completely rule out the possibility. I gather that there are multiple passages, and many may still be blocked by fill that was dumped in the past. 3000 GPM is 375 CF per second, which is enough for a modest creek ( I can't find a picture of drainage from Santa Rosa, but something like this:
http://www.americanwhitewater.org/photos/archive/medium/42597.jpg). In what I presume is a fairly arid region I'd expect that to result from either a large aquifer or a fairly extensive drainage area. That suggests that whatever is there is fairly extensive, at least from in terms of the hydrology.
Of course none of that guarantees that there's anything but small and miserable passage or that a risk/reward analysis means people should continue to search.