I've updated my comment above to say "and" instead of "or" as you're quite correct.

From the timeline of events (surviving initial onslaught, then falling over) I'd assumed that was a large part of the problem, people sitting on a live-updating map.

The browser is not the only place that can cache HTTP responses - proxy caches from the client's ISP and/or local WAN or corporate intranets should also obey caching rules in the HTTP response headers.

HTTP caching works. The problem with the bike share site in my opinion is instead of using established methods for scaling (like HTTP caching) and other good practices they reinvented the wheel as a Rube Goldberg monstrosity which, big surprise, didn't work.

Remember kids - don't scale until you need to.