The instructions say, pretty clearly, "copy and paste the article text you want to use", not "copy and paste some random guff you want to prove a point with". If you don't follow the instructions then, no, the results you get won't be valid. Surprise.
The rights they're granting you are clearly 'the rights not to be sued by AP for quoting their text', not anything else -- not rights against being sued by any third party or anything else. It's rights licensing, not insurance. Likewise, if YOU screw up the building permit form, yes, the city are within their rights to let you swing in the breeze as far as I'm concerned. But if you didn't then, sure, they'd better honour their commitment, as (hopefully) AP will.
It's a braindead web app, yes, and AP do a bunch of other stuff that's dumb and/or evil. But claiming that it's some elaborate IP fraud scheme to allow a stupid web app to accept incorrect input and print out some boilerplate text around it is a cheap shot, and dumb.