This allegation comes from Prof. Rajeev Kumar of IIT-KGP, whose RTI application brought to light the horrendous problems in the 2006 JEE -- both Charu Sudan Kasturi and Manoj Mitta have covered these problems extensively in the Telegraph and The Times of India. Rajeev Kumar has collected enormous amount of information both about the 2006 JEE, and its 2007 and 2008 editions. Check out this blog which is devoted to a discussion of his findings.
Thanks to Rajeev Kumar's RTI activism, JEE-2007 and JEE-2008 have been far more transparent, and this trend is likely to intensify with time.
But the problems in JEE-2006 uncovered by Rajeev Kumar remain unresolved. The Calcutta High Court ruled against the view that IITs should make amends by correcting the JEE rank list -- removing some people and adding others. I would guess (but I'm not sure) that this ruling is being appealed in the Supreme Court.
One of Kumar's allegations is that JEE-2006 was rigged to favour children of (some? certain? influential?) IIT professors -- more specifically, he suspects that the Chemistry answer scripts were tampered with.
Take a look at this post (it's a long post, but you will have to scroll down to Section 3 -- "Eliminate possibilities of tampering ... ) which presents a lot of circumstantial evidence to bolster his case.
The most damning is the one about IIT-KGP's "revelation" that it shredded the JEE-2006 answer scripts in late 2006 -- against its own explicitly stated policy of preserving all exam-related documents for a year. More importantly, this "shredding of evidence" happened while the institution's actions on many aspects of JEE-2006 were being questioned through a legal case.
You should not be surprised that the destruction of JEE-2006 answer scripts was revealed only with the help of the Right To Information Act.
Do read that post and decide for yourself how strong the case really is. I would take his evidence quite seriously because (a) he has been pursuing this case against his own institution -- openly, and through our courts and information commissions -- possibly in the face of opposition from his colleagues, (b) he has been proved correct many times, and (c) IIT-KGP hasn't covered itself with glory through its post-JEE-2006 actions (the shredding of answer scripts is quite revealing).
And I would add that, to my knowledge, he has not been sued by the IITs for disseminating false / defamatory information about them.