owning your domain and having control of a domain through a trusted registrar is better than relying on the worlds largest advertising company to manage your digital identity (email), which is offered as a free service, that's subject to a catch-all ToS.
An isolated fail in 2014 by one vendor, primarily due to poor support processes, is not a convincing argument to keep all digital identities in Google's possession.
There's also the risk of Google shutting down your account because you do something they don't like. This will lead to a similiar outcome and you won't have any recourse.
I think that GP's point is that "safe" is a tricky word to use when your data is in the custody of the world's largest non-governmental surveillance network with a a catch-all TOS.
