What I find amazing here is the idea that the creators of a work have no say in how it's used.
If this were simply a matter of copyright, then yes, you could claim parody. However, in 2012 when Adam Yauch passed away his will specifically mentioned "in no event may my image or name or any music or any artistic property created by me be used for advertising purposes." At the time, Forbes Magazine had an article on if this was even legal, which I'm guessing was the source of the brilliant idea to push it.
At the same time, GoldieBlox did not significantly change the tune, merely moving it up the scale. Given the response, I think it's fair to say that none of the band members gave permission for it's use. And the companies own actions show that they thought that what they were doing might be illegal, hence the "sure them before they sue us" mentality.
This breaks down to the copyright law in it's most base for. Does the creator of a work control it's distribution and destiny. If you listen to the freetards and their idea that "data can't be stolen, only copied", then the logical conclusion is that no, the creator has no say in how a work is distributed or used after they create it.
OTOH, it's not that the creator in this case refused GoldieBlox the ability to use it. They have consistently refused ANY request. Since they have refused all requests, and have a published history of doing so, then it would be reasonable to assume that they would also refuse "GB". At that point, using it anyway, is a gross violation of the creator's rights, as spelled out in the law.
Suing someone because you wish to violate their rights is just a kick in the nuts.