> what kind of company would fire me for "Alright love, you want a pizza..."
Many companies use those kind of rules, however, to fire people that are already in their cross-hairs. If a server logs the message, and employee handbooks says, "personal email blah, blah, blah"... it is pretty cut-and-dried from an HR-drone point of view and much easier than firing someone for the things they _really_ did.
But generally, employment in most european countries is not as tenuous as you suggest. You need valid reasons to get rid of someone, and usually you need to give the employee fair warning and a reasonable opportunity to improve or correct the issue that led to the warning. Nobody gets fired for sending a single email even if it's in violation of a clear company policy.
Things they allegedly did. Easiest way to avoid paying severance is to have something clearly black and white, otherwise court fees can add up.