Can you help me understand this word?

Frank Rich in the Sunday NY Times on 10/28/07 wrote this sentence: “You have absolutely nothing to fear from me,” Rudy [Giuliani]disingenuously told the assembled at the Values Voter Summit last weekend.

I understand the definition from American Heritage Dictionary: 1. Not straightforward or candid; insincere or calculating: “an ambitious, disingenuous, philistine, and hypocritical operator, who … exemplified … the most disagreeable traits of his time” (David Cannadine).

Wouldn't the root "genuous" mean true, so in-genuous mean not-true (for example, in-sincere). So would dis-in-genuous mean not-not-true, a double negative? Just wondering.