Hey Catherine,
I had to read your post about 5 times before I understood it. Let me see if I understand correctly. Badiou seems to be saying, and I'm reading him completely out of context as I haven't read him at all, that essentially there is no  more censorship, and that without censorship,  Art and even thought can not exist. He then recommends to add a sort of self censorship so art can exist.
Then your question is do we agree with him that the situation nowadays is that there is no censorship.

Of course I'm flattening things, but in general this seems to me your question.

Some notes.
First, his claim is reminiscent of Foucault's view of eroticism, but I won't go into that.

Second, he is not exactly saying that there is no censorship but a more complicated:  control by means of "commercial circulation and democratic communication."
(This reminds me of the difference Agamben, who quotes somebody I can't remember at the moment, makes regarding how our voting today is essentially a poll and not a real choice. The difference between the two is somewhat elusive and hard to explain, but when you get it, it is quite interesting.)

To give a crude, banal, reading of him, we can say that today it is not that you are not allowed to paint a penis, but painting it would limit who and for how much you would sell it for.
This is very different from saying you can paint anything. He uses the word censorship as something stronger than getting an x rating.

Now you see that the question becomes not whether he is correct about our times, but whether he is correct about the past? He seems to assume art, and thought, once existed. Perhaps even existed in the not too far past. Well, was the situation different at the time?
Yes and no. This seems to me a VERY complicated question so I won't enter into it here, but this is the question. If you think it was really the same, then his case is baseless. If  you agree, then perhaps he has a case.

One last remark - he doesn't have a case. At least not in any meaningful way. Whatever good art or thought was produced in the past we can claim came from self-censorship, and whatever is good now he'll claim self-censorship. Hence there is no scientific claim here, but a philosophical one. A claim of difference between our time and the past with regards this question.
What was the censorship of the greeks one might ask?

Very interesting topic it turned out to be. I also found Catherine's post quite hard to figure out.

I agree with what you said John, but want to add a thought. I totally disagree with Badiou's basic premise. I think for all great art and thought a freedom is necessary. A complete freedom who few manage to achieve. A freedom at least in the domain of the particualr thought. Afterwards comes the commercializing and thinking what one has to hide from the public, and how to sell it to them (as Descartes said: I advanced disguised).
Rousseau has this beautiful image saying that to get people to drink medicine you spray some sugar on the tip of the glass. That's what they taste., and don't feel how, on the sly, you gave them medicine. This is what some thinkers know how to do. But it is folly, or rather total ignorance, to think it comes from them censoring their taste. To think that the thought came from a prohibition. It is actually rather sad to know some people think this. But then, to quote Rousseau again, which is so fitting here, (an imprecise quote from memory from the social contract): Man is the only animal born free but who constantly wants to chain themselves.
This seems to me precisely Badiou's move.

(A disclaimer: These quotes are from memory and are not precise. Also, I don't know Badiou much and my reaction is to the specific thesis discussed and not a general remark regarding him. It might be a misunderstanding?)

I don't know much about Badiou either, but I read the quote differently (though in any case no reason to derail an interesting discussion).

It seems to me that he is making a panopticon kind of argument. i.e., we live in a semi-totalitarian society in which thought is controlled so seamlessly that it is possible to experience ourselves as having complete freedom, because rather than holding all possibilities in the mind and realizing that some are not possible, we simply forget that these alternatives exist.

Obviously this dooms the creative thinker and the artist. So if you do not want to live this way, you must consciously begin to develop your sense of the outside (even if it is by dividing just those courses of action you can conceptualize at this moment into available and forbidden), as a way of building up your own sense of self rather than passively accepting the dictates of Empire. Presumably this is a first step in becoming/staying human, and in Thesis 15 there will be more to do.