Regardless of the legal standing,

It is ridiculous for Moveon.org to restrict the use of its name in a political advertisement, and it is ridculous for Google to stand behind this policy as a shield, when it could easily clarify that the policy doesn't apply to registered political organizations. This is much different than a company trying to protect the integrity of its trademark. Moveon.org participates (and IMHO rightly) in the political debate using its resources to run advertising and support causes/candidates it wants to.

This is different than use the coke logo in a google add that says "Coke Sucks!" Failure to properly identify the organization in the ad means the ad has no meaning.

This is typical of the doublethink - only for free speech when they like it - Moveon.org is a joke!