Ah, okay. I've never flown a Sea King, though I have landed a Bell 206 in the water a few times (happily, inflated floats are hard to fill with water!). But I know some about the drag of a hull in the water, particularly moving forward under power, with a high trust line, and the landing gear down. In the case of the Russian MIL, it appears that the wheels extended when it hit the water (perhaps the pilot was unaware), so moving forward with the drag of the wheels extended under the hull would have similarities to snagging a wheel or skid on an obstruction on the surface while drifting laterally.
But yes, the C of G change from a flooded nose compartment would do it too! I have had flooded float compartments on a floatplane, though there are different opportunities to manage that a little better.