Well, the point of introducing the cost limit for the car, as explained in the episode, was that the car has always won these races so far, so they intended to make the car fight with one hand tied to the back to make the race more difficult for it. Of course, as demonstrated in the piece, getting loats of horsepower for little money is still possible, and horsepower doesn't really decide who wins either. Therefore this cost limit is more or less window dressing, but the idea still stands.
I don't want to go into the details, so here are my 2c: I work for the German branch of an American company. We both develop products for our individual markets, and naturally, we also share products from time to time. Now, the majority of American products we are asked to introduce to the German market needed at least a major makeover, sometimes a complete rebuild. The reasons mostly are quality and useability issues.
The American products we get always look good on the outside, have nice surfaces and a good feature list, but when you take them in your hands and start to use them, you notice that there is little substance behind the surface. As a conclusion, it appears to me that a "quality product" to an American is something which has a lot of good features and looks good. In contrast, a "quality product" for a European (speaking for the Germans here) is something which is built well in every single detail and also down to the very core. It doesn't need to have an endless feature list, but when you use it, you must feel it was engineered from the ground up to be a quality product, and that a lot of thought has gone into even the tiniest detail.
That is what Clarkson is on about when he criticises America. He criticises that things look good on the surface, but start to fall apart (figuratively) as soon as you lay a hand on them. That there is no substance behind the shiny surface. That of course does not expand to all branches of engineering, and also he does not say that Americans are not able to engineer quality products. But it applies to many products of daily life. Let's stay with the Ford Mustang as an example. I personally know two people who have had the current V8 Mustang as a car. Both said that it has a lot of power, which is nice. And then, both sold the car much sooner than they initially intended to, because they said it is so hard to control on a wet road even if you just want to drive normally that they were too scared to do so, which in turn meant that they didn't want to live with that car. So on the surface, you get a car with loads of power for little money, which seems very attractive to any car enthusiast. Nonetheless, if it turns out that you can not really use that power and that it is rather disturbing than helping in daily traffic, there is little point in having that car. As a product for the European market, the Mustang would never have seen the light of day, simply because it is not refined enough for the European market. That is exactly what Clarkson concluded.