I can't give you as erudite an answer as the others, but I can address your two specific questions about the Qur'an. My main reason for offering this answer is that a significant portion of those who watch TED talks are non-Muslim Americans who have almost zero familiarity with Islam, and the familiarity they have is usually based on wild propaganda.
So in case you (or anyone else reading your question) find it useful, here is the perspective of a non-Muslim American who has read, from begining to end, multiple times, various English translations of the Qur'an: Arberry, Pickthall, Rodwell; recently begun studying the hadith; and supplemented the study of the Qur'an with an English translation of Tafsir Ibn Kathir.
The tiny fraction of TED viewers who have any familiarity with Islam will likely have scanned (not read) one of these translations, will never have read a single hadith, and will never have even heard of a tafsir. Further, almost no one realizes the importance of the hadith. The average American would have no idea what a Qur'anist is, and if you told them what it means, they would think all Muslims are Qur'anists.
As for the number, I have carefully combed the Qur'an for the number 72. It is not there. There is not even a hint at there being a limit on the number of virgins you can have.
As for bosomly shaped women, it is important to understand that Christianity still has a strong influence on the way Americans think, even if they aren't Christians. Christianity traditionally has had a rather dim view of sex; note the fact that Catholic priests are required to be celibate, for example. The fact that there is sex in the Muslim Paradise is therefore scandalous. It wouldn't matter much whether your virgins were exceptionally voluptuous. I count seven suras that talk about virgins in Paradise. Presumably Hazleton is referring in particular to Sura 78, which in English is called The Great Event, in verses 31-33:
Arberry says, Lo! for the duteous is achievement / Gardens enclosed and vineyards / And voluptuous women of equal age
Rodwell says, But, for the God-fearing is a blissful abode / Enclosed gardens and vineyards / And damsels with swelling breasts, their peers in age
Pickthall doesn't describe the virgins: Lo! for the duteous is achievement / Gardens enclosed and vineyards / And maidens for companions
The words voluptuous and swelling breasts are the only words that would be heard by most non-Muslim Americans. And it would be taken in a very sensual way. Further, it would make little difference whether this description were included; the key point is the fact that seven surahs indicate that Muslim men will be given an unlimited number of sex partners.