Question:

Did Van Jones really sign the petition in question?
One can go to archive.org to check out old screen shots from different web sites. If one looks at the Dec 3, 2004 archive of the 911truth.org website and clicks the link about the 911 Truth Statement they will see the following items on a list:

web.archive.org

45. Randy Hayes, founder, Rainforest Action Network, US National Director, Direction Conservation
46. Richard Heinberg, author, The Party’s Over, core faculty, New College of California
47. Van Jones, executive director, Ella Baker Center for Human Rights.

Conclusions:
1. It is probably accurate to say that a petition existed back in 2004 with Van Jones’s name on it.
2. This petition did exist at the 911truth.org website, unless someone hacked the database at archive.org.
3. Although it is possible that the website co-opted Van Jones name, this would have had to take place in 2004, which would probably be unlikely.
4. 911truth.org states that this petition is accurate.

It is probably safe to assume that Van Jones did sign the petition. Now, it is true that he may not have known what he signed as he is a person who gets involved in many political causes. Two points of mitigation here is it seems unlikely for a well respected lawyer who graduated from Yale would not know what he were getting into. One would expect such a person to understand what it means to sign a petition like the one shown at 911truth.org. Also, it is reasonable to point out that Van Jones has not denied the truther movement (to my knowledge) prior to any point up to tonight.

Draw your own conclusions from my message, but I would favor the Truthers on their veracity that Van Jones signed their petition.