The problem seems to be that in German, the term in reference to soccer broadcasts is countable, an event, not just a verb. You could say in English 'The pub will be open for public viewing of the soccer match,' but it would be better to say 'for the public to watch the soccer match,' and surely you would never advertise 'a public viewing.' So even though there may be infrequent occasions when the two terms overlap, they're far more often false friends.
Precisely because there have already been so many questions in the forum, and this comes up every year at tournament time, it seems to me that it would help to at least offer other suggestions for translation. Just warning users against a (usually) false friend isn't very helpful if we can't offer any better alternatives.
And in fact, there are a lot of other choices, almost any of which would surely be preferable. What about, for example,
closed-circuit video broadcast
I personally could at least support 'live broadcast' as a starting point. It just seems to me that it would be better to put something in the dictionary than continue this endless series of forum discussions, people referring other people to forum discussions, and so on.
OT: I've said this before, but I still think it would be really wonderful if there were an automatic script to convert any URL that links to forum search results. I think it would only need to say something like 'Siehe Forumssuche' in bold (instead of 'Siehe auch' for a forum thread, or 'Siehe Wörterbuch') and strip out the parameter PHPSESSID (which we still have to do manually, which is still a nuisance).