AWS is incidental to both the problem and solution because the problem is an authorized and legal government program. No matter who holds your data, it will be subject to the same access if the government wants it.
There are only two solutions:
1) Encrypt your data before sending to the cloud, so that server access becomes irrelevant. (This is what Tarsnap does.)
2) Change the law to stop or change the programs.
Neither can be accomplished by Amazon or any other single provider.