SHOOT SHOOT SHOOT. I was totally wrong about the radio guys. I just re-listened to the whole show podcast and realized I went off without the right information. They told this woman's story very well:
Here's the link to that story.
I'm a breastfeeding mom, but I'm not militant about it. In that situation I would have done the exact same thing- those blankets are gross and there is barely enough room to get everything in place without one. Many kids (like mine) will pull down a heavy blanket and refuse to eat under something like that. In the end, her reasons for refusing the blanket are unimportant: she has the right to feed her kid within reason, and the airline personelle was out of line both legally and on a customer service level.