I'm kinda suprised to hear this about American Eagle .22's. I own a few .22's and never noticed any issues that I haven't had with any other cheap .22 ammo that I own.
I just bought a few boxes from the sporting goods store a couple of days ago and took a look at it.
The .38gr HP's copper looks a little tarnished but they are not loose at all.
The 40gr lead seems to look fine and are not loose either.
I avoid remington ammo as well. Their quality control has really went downhill.