PETA is at it again

In response to the new TSA scans, in which people must go through an invasive full-body scan in order to fly on an airplane, PETA has released a new and insulting ad:

There is a lot that is wrong with this ad. It makes many assumptions, such as:

• Being vegan will necessarily make you healthier.
• Being healthy necessarily gives you a thin, "sexy" body.
• Vegans and/or healthy people can't be fat.
  
• The only reason people don't want to go through the TSA scans is because they are ashamed of their unattractive bodies, not because it is an invasion of privacy that many people are not comfortable with.

The last one is especially annoying to me. There are so many reasons people might not want a random person to see them naked; chances are it is not because they are embarrassed about how fat they are. I think PETA knows this, and they are making light of a serious problem and using it to further their agenda (and I'm not implying that there is anything wrong with their agenda, but the TSA debate has nothing to do with the ethical treatment of animals). Luckily, most airports refused to post these ads because they do not want to take a political stance on animal rights. That is the wrong reason for doing the right thing. These ads are meant to shame women (I wont believe that it's just a coincidence that it is a woman's body in the picture). Putting these ads out further contributes to the idea that women's bodies are public property, which is exactly what is wrong with the TSA scans in the first place (of course, both men and women are being subjected to TSA scans, but the scans are treating people's bodies like government property. And victims of sexual assault, which is usually women, are less likely to be comfortable with the body scans).
Question: Why is PETA the most well-known animal rights group if their methods of effecting change are so problematic?