That's not it. It's just garbled. "availability heuristic" means that recent or related-to-current-situation events are easier to remember than other, so they bias your mental estimate of "average" or "sum".
No, the GP has the right idea. The availability heuristic also causes emotionally-potent events to seem more recent than they were, because they're "available." Because recent events are easier to remember, our brains assume incorrectly that easier-to-remember events must be more recent. When, really, there are other reasons an event can be easier to remember.
This is the logic behind the "climate of fear" the media creates—every time a tragedy is made into a huge news story, it becomes semi-permanently available as an exemplar to your brain of that kind of thing happening; and then, when you try to figure out when the last time that kind of thing happened was (which is, in turn, a heuristic people tend to use for how often something happens) the highly-available exemplar in your mind makes you still feel like it "just happened" even if it was years ago.
(Or, to put that another way: everyone in America who was alive when 9/11 happened, still thinks of terrorist attacks against the US as happening far more often than they do; everyone in America who was born after 9/11 has a better-calibrated estimate. The scope of the tragedy—and especially of the reporting of the tragedy—caused it to be "too available" to people, permanently biasing their time-scale and frequency estimates.)
