Apple Watch never checks for heart attacks

The health data is automatically added by the watch. If you can see heart rate data, this means your Apple Watch is sending data to the Health app properly.

The message on the screenshot you posted is a bit misleading. In this answer you'll learn how to verify that the heart rate data is being transmitted correctly and how to shut off heart rate data collection.

Seeing Heart Rate data

Open the Health app on the iPhone. Select the Health Data tab. Navigate to Vitals > Heart Rate:

If you see data, that means your watch is properly sending data to the Health app. You can make this visible on the initial screen for the Health app by toggling the Show on Dashboard switch.

Disabling Heart Rate data

You can turn off Apple Watch health data collection. Open the Apple Watch app for iPhone. Select the My Watch tab. Navigate to Privacy > Motion & Fitness. There, you can turn off Heart Rate or Fitness Tracking:

If the watches are different, and the phones are different, then the only thing that appears to remain the same is you.

You don't mention, but have you ruled out the possibility of there being anything about you? For instance, I remember reading that tattoos could prevent the heart monitor obtaining a clear reading, and there was some talk about people with very black skin also having difficulties. Example article here http://www.bbc.co.uk/news/technology-32537030

The other possibility is whether there is something with the tightness with which you wear it?