In my agency, as a general rule, every text gets proofread -- at least those from German into English, which is the field I work in, but I'm pretty sure it holds for the other major languages. Most of our translators are very good and are carefully selected (I've known a number who didn't live up to expectations during their "Probezeit." They're justifiably no longer with the company...
Once in a great while, a contract goes through without being proofread. That's either due to lack of time, or because the customer really only wants/needs a rough translation to get a sense of what the item is about.
When I first started proofreading, I used to do more rewriting than I do now. If it's not incorrectly translated or poor English, there's no reason for me to bring it into "my" style. When it comes to the final product, however, the translators don't have much say in the matter of what gets done with "their" translation; in the end, it's the proofreader who is responsible for the final text, and if a customer complains, the proofreader has to take care of the problem.
It's not that unusual that we get a job from a customer that only requires editing/proofreading -- the customer has taken care of the translation. In the best cases, the proofreader receives the text in both the source and the target languages, and the customer had a competent native speaker do the target language. Those are usually pretty easy, but are extremely rare. More often, you get the feeling that it was a non-native speaker who did the translation, likely a non-translator within their organization. If you're lucky, the translation is still OK, but it requires more work. And then you get those translations where it appears that the boss's niece or nephew, who happens to be studying English at the Gymnasium and spent six months in the UK or the USA, did the translation -- you can only hope that you don't have to retranslate the entire text yourself.
The worst case? When the customer doesn't provide any source text and you have no clue as to what they're trying to say because what you're working with is so poorly written. If you request the source text, the customer says that there isn't one: A NNS in their firm wrote it in English directly. Still, it's your job to try to rescue it. Often, the deadlines for such jobs are very tight, and there is no time to query every point you can't make out. If that's the case, sometimes the best you can do is mark/highlight the worst of the spots and deliver with a note saying that the customer needs to look at them. I can't think of a time when a customer was dissatisfied with that approach. A couple times they have replied with an explanation of what the sentence is about so that the problem area could be fixed up.