> what kind of company would fire me for "Alright love, you want a pizza..."
Virtually no company would do it just for that.
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.
The case in question was 10 years ago in Romania, which was only just becoming an EU member that year. I have no idea what sort of laws applied at that time in that country.
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.
I don't use my work email for personal use, but what kind of company would fire me for "Alright love, you want a pizza when I am on my way back?".
What is next? "Excuse me Sir, Excuse me Sir, Can I go to the toilet please?" Fuck working for a place like that. Leave your dignity at the door.