The "lump" of rain was extremely heavy and from the way it snapped I will hazard a guess that one front and the rear aquaplaned at pretty much exactly the same time while the other front stayed on the road surface but with lots of drag from the water depth so the whole car just pivoted around it. I hit the opposite lock stop pretty damn quickly but there was no purchase on the road at all and I might as well have not bothered.
I would agree with the pull on the car.
I nearly had the mother of all accidents in our M3W. Much deeper than expected puddle on the kerbside at the bottom of a dip in the road. Oncoming lorry meant that where I would normally go around the puddle I had to go through it, and the car pulled round in one hit. Straight up and onto the verge, opposite lock and managed to bring it back. How I didn't hit the fence, hedge/roots or over correct and spear across the road I have no idea. A bit of skill and an awful lot of luck. I certainly wouldn't fancy my chances if it happened again. This was on the factory Avons with good tread.
I certainly take even greater care with standing water & the M3W than I used to, and I was already careful to start with.