I find it interesting that you're getting consistent downvotes for saying the same thing my startup's legal counsel has repeatedly said about the AGPL: Be extremely careful. Assume nothing and write defensively, because the nature of an "integration" is too vague to risk a company's infrastructure.
I get the impression others here are happily screwing around with AGPL integrations with nothing to lose.
I wonder what the lawyer would say about a startup agreeing to EULA's in gmail or iphone/android. Im sure there is not vague terms in those contracts, and that customer emails is perfectly safe to be stored there with no liability risk to the company.
I only suspect, but I think that vague terms in contracts is less of an issue when there has been no court cases involving companies that followed standard practices regarding compliance.
I get the impression others here are happily screwing around with AGPL integrations with nothing to lose.