What was claimed
If your email gets hacked, Google Authenticator 2FA synced to Google cloud/account is compromised; everyone should immediately unlink from cloud, use local only, and securely store backup/recovery codes
Our verdict
Needs cautionThis is not a universal best practice supported by the sources. Google says cloud sync is optional and designed for restore convenience, so whether to use it is a tradeoff, not an across-the-board requirement. A compromised Google account can expose synced Authenticator codes, which is a real risk. But the statement is too absolute because it depends on whether Authenticator sync is enabled and whether the attacker actually gained access to the Google account used for sync.
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Key findings
Everyone should immediately unlink from cloud and use local only.
If your email gets hacked, Google Authenticator 2FA synced to Google cloud/account is compromised.
Use local only
Backup/recovery codes should be securely stored.