I think the summary is a bit
too sensationalistic in terms of what the actual security implications are:
The Heartbleed bug allows anyone on the Internet to read the memory of the systems protected by the vulnerable versions of the OpenSSL software.
Yes, while that's true, it's not a "read the whole process' memory" vulnerability which would definitely be cause for panic. The details are subtle:
Can attacker access only 64k of the memory?
There is no total of 64 kilobytes limitation to the attack, that limit applies only to a single heartbeat. Attacker can either keep reconnecting or during an active TLS connection keep requesting arbitrary number of 64 kilobyte chunks of memory content until enough secrets are revealed.
The address space of a process is normally far bigger than 64KB, and while the bug does allow an arbitrary number of 64KB reads, it is important to note that the attacker cannot directly control where that 64KB will come from. If you're lucky, you'll get a whole bunch of keys. If you're unlucky, you might get unencrypted data you sent/received, which you would have anyway. If you're really unlucky, you get 64KB of zero bytes every time.
Then there's also the question of knowing exactly what/where the actual secrets are. Encryption keys (should) look like random data, and there's a lot of other random-looking stuff in crypto libraries' state. Even supposing you know that there is a key, of some type, somewhere in a 64KB block of random-looking data, you still need to find where inside that data the key is, what type of key it is, and more importantly, whose traffic it protects before you can do anything malicious.
Without using any privileged information or credentials we were able steal from ourselves the secret keys
It really helps when looking for keys, if you already know what the keys are.
In other words, while this is a cause for concern, it's not anywhere near "everything is wide open", and that is probably the reason why it has remained undiscovered for so long.
Edit: downvotes. Care to explain?