But you said "AGPL". AGPL SAAS running on someone else's computer that you can access requires that they provide you with the source code they're running. Barring shenanigans, that source code would enable you to run the same SAAS yourself if you desired to do so.
I'd say having the ability to run the program locally _and_ its source code is "more open" than just having the ability to run the program locally in binary form. With AGPL in your scenario you get all three of source access, local execution, and remote-SAAS exection. Proprietary local code you get one of those three.