She wants to clarify Islam to us unbelievers, yet she isn't willing to wear a veil? How can we believe what she says? Maybe I just don't understand Islam.
FYI
Encycloaedia of the Orient
hijab
http://lexicorient.com/cgi-bin/eo-direct-frame.pl?http://lexicorient.com/e.o/hijab.htm
Head scarf used by many Muslim women, generally intended to cover the hair. The hijab has in recent decades more and more come to be associated with Islamism, hence it is partly prohibited in some Muslim countries, like Tunisia.
Hijab comes in numerous fashions, several of these have backgrounds with specific countries, regions or ethnic groups. It is assumed that these variations of the hijab are continuations of pre-Islamic customs, but adjusted to the regulations of Islamic theology.
The head scarf is not uniquely Muslim, it is also found in Judeo-Christian traditions. It has been, and is, worn by adherents, with nuns as the most distinct example, and it is mentioned in Biblican texts, like in Paul's first letter to the Corinthians 11:5, where women are commanded to cover their heads when practicing their religion, or be punished.
It is assumed that sura 33:59 in the Koran orders women to wear hijab, but this passage is open for alternative interpretations. A slightly clearer command on using the hijab comes in the hadiths, but even this cannot be concluded to imply a general obligation for a Muslim woman to cover her head, as it really only refers to the wives of Muhammad.
Koran sura 33: Confederates
59 O prophet! Tell your wives and your daughters, and the women of the believers, to wrap their veils close round them. It is better that way, they can be recognized but not annoyed. God is forgiving and merciful.
Koran sura 24: Light
31 And say to the believing women that they cast down their looks and guard their private parts, and display not their ornaments, except those which are outside; and let them pull their kerchiefs over their bosoms and not display their ornaments save to their husbands and fathers, or the fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or their brothers’ sons, or their sisters’ sons, or their women, or what their right hands possess, or their male attendants who are incapable, or to children who do not note women’s nakedness; and that they beat not with their feet that their hidden ornaments may be known. But all turn repentant to God, O believers! May you prosper.
Bukhari, Volume 1, Book 8, Number 395
2 And as regards the (verse of) the veiling of the women, I said, 'O Allah's Apostle! I wish you ordered your wives to cover themselves from the men because good and bad ones talk to them.' So the verse of the veiling of the women was revealed [probably the following].
Koran sura 33: Confederates
53 (...) And when ye ask them for an article, ask them from behind a curtain; that is purer for your hearts and for theirs. It is not right for you to annoy the prophet of God, nor to wed his wives after him ever; verily, that is with God a serious thing.
Koran sura 42: Counsel
50 It is not for any mortal that God should speak to him, except by inspiration, or from behind a veil
From the Koran 33:59, it may appear that a woman not in danger of being annoyed, does not have to veil herself. Moreover, the Arabic word translated into the English "veil" is actually not "hijab", but "jalãbîb", a plural form of "jilbab". A jilbab would normally be translated into "woman's dress", a dress that covers most of , or the entire body, and not necessarily the head. Hence it is possible that this aya does not requisite women to cover their hair or even their faces, but to wear the body garment in such a way that they cover and hide erotically laden parts of a women's body, like her breasts.
In the Koran 24:31, often the preferred aya for proving the need to wear the hijab, the word in question is here is "zîna", and can be translated with "ornaments" or "jewels" or even "clothes". This is by some Muslim commentators believed to be understood as hair, but seen from the context it appears a woman's nipples is a more correct translation. The hair theory seems farfetched.
While hijab today is commonly used for the head scarf alone, hijab is fundamentally any partition which separates two things. In the Koran 33:53 "hijab" is used, but not denoting a head scarf, but a curtain behind which Muhammad could hide his wives from other Muslims. Another use of "hijab" is found in Koran 42:50, where it is told that the hijab separates man from God.
(note: Encycloaedia of the Orient, I've found it to be a pretty good source of info.)