I'm gonna go out on a limb.

I'm in the "your heart rate monitor was EXACTLY RIGHT" camp.

What does a quick spike on a HR chart mean? It means that, for the interval your HRM is set to (1 sec? 2 or 3? 5?), your heart beat really fast. Maybe you somehow got 4 into that one second for whatever reason. It only lasted a second, but your HRM picked up on it and you have a huge spike saying you were at 240 BEATS PER MINUTE!! But you weren't. You were at 4 beats per second, for one second. Before and after, you were likely lower. Who knows? Maybe you even had a PVC (a premature beat we all get from time to time for a huge variety of reasons) during that little window your HRM was listening.

The important thing is that it was not sustained, you had no repercussions from it, and you're listening to your body and your doc. Keep it up and don't worry about the little blips on your graph that don't seem quite right. No one has a smooth graph.