Yes you are missing something: HR IS NOT YOUR FRIENDHR IS NOT YOUR FRIEND
Every last meeting like this, they are building a file on you. The proof of this is the tone of the last meeting demonstrated. The next step is likely to start requiring doctor's notes.
The fact that they suggested you might be attending sporting events indicates that they are VERY suspicious of you and are taking an adversarial stance. If less work meant less sickness, then pensioners should be immortal by that reasoning.
Something not good is going on, it sounds like you are being targeted for disciplinary action. You may be dealing with an office gossip as well. Where did they get the idea that you are not sick on your sick time?