I wouldn't be too worried about the core equipment as far as the Heartbleed vulnerability is concerned, as this issue pertains to equipment that is responsible for making secure connections across networks. ASAs, Firewalls that can act as VPN endpoints, Wireless Access points with tunnelling support, and so on. None the less, providers like Verizon will all have to upgrade affected gear considering the nature of the bug unless they want to put all of their customers at risk.
Externally, Verizon's websites should all be patched as they're hosted through Akamai. auth.verizon.com is not showing as being vulnerable. Internally, that should be all patched but will likely not result in any sort of answer. As for the BHRs on Port 4567? STARTTLS is being a pain to test at the moment with the current tools. Guess your best bet is to look at the source code for them on ActionTec's website to see what's included.
I'd be more worried about the network getting poisoned through BGP attacks :)