You are certainly more likely to fall when standing, than when sitting. However, the original quote didn't mention anything about you falling over - it was talking about safety. You can argue all you like about degree (and I do), but it is obvious that, in general, 1000 people sitting is more conducive to safety than 1000 people standing.
Fighting the guidelines on those grounds is a waste of time. The question should not be," is it safer?", but rather "is the extra safety worth the additional cost and inconvenience to the fans?"