If another P2P, or other network, could put up the same hardware and energy for secure, anonymous transactions then their digital units may have similar value.
agreed, but the similar value in question may be zero, or any other number on the 'value line'.
security is a 'necessary but not sufficient' condition for establishing currency value.
demand-binding is also a necessary but not sufficient condition.
likewise, scarcity.
I guess that's another reason to get people using btc for g&s on the internet, especially for net-based services to which btc are particularly suited.