No one ever said that AMD's CPU's are 'untouchable' by potential security exploits... however, AMD remains LEAST AFFECTED (at least compared to Intel), and are usually quick to respond with security patches.
The sheer amount of security vulnerabilities that affect Intel are usually more important for servers and data centres (where big money is).
On an individual user level, a person is not very likely to encounter issues related to these exploits... however, out of the two, Zen uArch is (and I am repeating myself here) 'least affected'.