This is what I would assume, but has it been confirmed that this vulnerability doesn't affect identities provided by an SSH agent? If any of this "roaming" support was provided by the agent, it could be the case that the leakage can be triggered via SSH agent protocol requests. I doubt this is the case but I don't see anything confirming or denying it.
It would be nice to hear some official word on whether agent-based authentication is vulnerable, because if it isn't, the seriousness to me is greatly reduced, as I never load identities in the client directly.