I checked that link again.

And sure enough it does apply to Android apps. To wit, this passage.
"Clear your device's Calendar application data
Warning: After performing the following steps, events from more than 30 days ago will no longer be available for viewing on your device. Rest assured these events remain saved on the main Google Calendar server and are accessible via the web. Further, these steps will cause your Calendar app settings (e.g., Calendar notification ringtones) to be reset.
We recommend proceeding with these steps only if the above steps did not resolve the issue.

Press your device's < Home > button, then press < Menu >.
Select Settings.
Select Applications, then Manage applications.
Select Calendar Storage.
Note: If you don't see 'Calendar Storage,' press < Menu > again, then select Filter > All. On some devices, you won't see 'Calendar Storage.' It is fine to ignore this step if it doesn't apply.
Select Clear data. Answer OK when prompted.
Restart your device. Press and hold the < Power > or < End call > button, then select Power off. Press the < Power > or < End call > button to power on.

Your device will re-sync with the server after restarting (this may take several minutes)."

And there you see the steps to clear the app data.

I'm not disagreeing with you that this should be a lot better.