>there was a rich woman that drove into a lake on her estate and drowned because she couldn't open the door in time.
Just to expand a bit on vkou's sibling reply, exiting a car that has already gone under water is absolutely non-trivial in any vehicle. Water pressure goes up very fast with depth: at just 10' (3m) deep, just minimum recommended depth for a simple outdoor low dive board pool, you're already at 4.25 psi. At 16.5' (5m) you're up to 7.1 psi.
Just using a tape measure on a more compact car (not my truck) our in the parking lot, a GTI mini, front door is ~1680 in^2 in surface area. So you already cannot open the door if it's air inside and water outside and you're in even 10' of water let alone more. My recollection from driver's ed and then emergency response is that you're supposed to get the window open (by lowering it in time if electric or unshorted or more likely by shattering it with the emergency tool you hopefully have in the car) and let water fill the interior to equalize the pressure, trying to get a last breath from the bubble at the top as long as possible. Then you've got a breath-full-of-air time to get the door open (or get out through the broken window) and get to the surface. And not lose your bearings if it's anything but shallow+bright sunlight, etc., easy to do under water when panicked if you're not well trained to instinctively do tricks like let out a small stream of bubbles to feel which way is up. It's a pretty frightening (and thankfully rare) scenario.
I think I vaguely remember the incident you're talking about, and bad doors certainly didn't help, but it's not the same impact as someone being trapped right on land where 99.9% of vehicles made in history would allow an easy exit.