In my opinion, there are good doctors and bad doctors everywhere and the US is no exeption. To say that ALL American doctors are good is imao just an oversimplification in order to subconsiously mask your fear of the unknown (obviously, it feels more comfortable to do it in your country with people of your own nationality in a familiar environment). I am absoutely fine with it, I think it is normal human behaviour (and also the basis of racism, I'm afraid) but for those who can overcome this fear, it may save them lots of money and years of saving.
I agree with you that in the US the medical profession is much more heavily regulated compared to some places like Turkey or Asia (and this may indeed make a difference in safety); but you can't really say the same for countries like the UK or European Union where practicing medicine is also very strictly regulated by the authorities.
As far as I am concerned, the best way to choose a doctor ( and I am not only talking about LL here) is to actually do your homework! Check their credentials, background and experience on the particular field that you are interested in. Check reviews from previous patients. Check the environment that they work in and talk to the doctor themselves to see how they communicate and relay information. This, imao, will lead to the best possible choice. If, after doing all this "homework", you can also afford the luxury of having your treatment done near you, that's even better!