For almost two months now, we can choose the profile to sync info with in our network profile. This is nice and welcome, however a less known side effect is mentioned in a comment: (emphasis mine)
Automatic sync is gone entirely, except for users who don't have a user profile on stackexchange.com itself. (FWIW, it was never automatic so much as triggered when someone visited the profile.) If there's a big demand for it, we can revisit this implementation
Most users are not aware of this. Long time users of SE still think there is auto update going on, i.e. that after editing their main profile (on the oldest site), the network profile will catch it and update all by itself, as it always used to be. A concerned user found a clear case of such unawareness.
What I suggest will nullify any possible damage, and should be simple to implement: when someone visit the network profile of a user, the system will check "Have this user ever manually updated the network profile?" - if yes, then don't do anything. But if not, run the old code of auto synchronize with oldest profile.
This way those aware of the change will manually update the network profile and it won't be overwritten, and those unaware won't stay with old and unwanted information in the network profile.