It's not even an issue of trusting Amazon. Or, just trusting their motives. You also have to trust their security on an ongoing basis, as your device could theoretically be compromised at any time.
While this may be true, I'd trust Amazon more than the various Chinese camera makers that offer cloud connected streaming and storage. Heck, I'd trust them more than my own ability to secure a vulnerability-laden home router that AT&T manages and probably never patches.