If the AGPL could prevent Amazon from publicly performing your software (let alone "using" it for SaaS, which is a hell of a lot more ambiguous), it wouldn't be

If the AGPL could prevent Amazon from publicly performing your software (let alone "using" it for SaaS, which is a hell of a lot more ambiguous), it wouldn't be any more DFSG- or OSI-compliant than the Commons Clause. As the other replies point out, the AGPL adds a copyleft clause that comes into play in these cases - nothing more than that.