I don't know the position of the bits in your engine, so some post-calamity evidence may be due to gravity rather than pressure, but what you have found - oil in water, no water in oil - would support the oil cooler failure. Oil is at high pressure, probably around 60 lb/sq in. The water at normal operating temperature would be at around 15 lb/sq in. So if the oil/water interface is breached, oil would go into the water at least to start with. It would also cause the water system to over-pressure massively and suddenly. So you would have a sudden rush of oil into the cooling system. This would overwhelm the ability of the pressure cap on the coolant reservoir to release the pressure, and so the hoses would be the next weakest thing to fail to release the pressure.
I think that the logic described above holds. Bearing in mind that I not know the engine.
Once the pressure in the coolant system has been released by the hose blowing off, the question of water getting into the oil would only depend on how much water is left, and whether that amount of water has settled at a point higher than the hole in the oil cooler.
I think my first attempt at diagnosis in this case would be to remove the oil cooler and either pour some thin oil into the oil pipes ans see if it comes out of the water pipes, or vice-versa, pour water into the water pipe and see if it comes out of the oil side. If it doesn't, I would try again with some sort of pressure test. Air would be good for that. Some inner tubing over the water pipes to the oil cooler and see if air comes from the oil side.
I would, at least initially, discount the head gasket. Even if they fail the hole is usually quite small and the excess pressure in the water would normally be released through the reservoir cap, the water would be released, there would be a hot smell around for a while before failure and the engine would be running unevenly. I don't think even a sudden head gasket failure would give the sudden catastrophic symptoms you describe. But if a quick oil cooler check doesn't immediately show a failure there, a head removal would tell you for sure.
You might even be able to check the oil cooler in-situ. From the picture it looks as if there are a pair of hoses on the water side, in and out, presumably. Do the other ends got anywhere accessible? If so, squeeze off (or disconnect and block) one of them, and pressure the other. If it doesn't hold pressure, the cooler has failed. If the breach is big, you may be able to do this by just blowing down the hose.
Good luck.