If all that happens is that the water fills up the exhaust pipe, perhaps no damage was done to engine internals. A few years ago, when samaritanizing some people in and around a flooded bit of road (I was in a lifted Jeep), some kids in a BMW 320i needed a jumpstart because their battery was rather puny, but in the course of a lot of cranking they disgorged all the water from the tailpipe and were on their way. Unfortunately a couple of people also flooded their intakes, a much different proposition. If you get a substantial amount of water high enough, the induction stroke lets water into the cylinders, but then the compression stroke -- whoa nelly! It's all the worse when everything is nice and hot.
One of them was in a minivan and believed in the popular idea that the way to take a water crossing is as fast as possible, lest you lose traction. Throwing a roostertail worthy of a ship coming off the ways, he sucked in rather a lot of water and only made it halfway. Had he taken it slowly, just fast enough to give himself the benefit of a gentle bow wave, he'd have been fine.
So I guess it comes down to how high your air intake is, and whether you sucked water into the cylinders and then tried to compress it. I can think of several ways that unexpectedly deep water might give your car starting issues, many of them electrical. So maybe you just lost your computer, or if you're really lucky you just have a saturated connector somewhere.
Before tearing down the engine, I'd pull the plugs and look around with a borescope, and see what can be done easily to get a similar glimpse of the overhead-cam area. And, of course, I'd drain the oil and see what it looked like. There is a possibility that you have internal engine damage, but also a possibility that you got lucky. Certainly I wouldn't take the word of a body shop unless they also have mechanical and electrical expertise and have gathered some of that kind of evidence.
Cheers,
--Joe
PS. I'd examine the fluid in the transaxle too; and did the brake master cylinder or the power steering reservoir get submerged?