In the Netherlands we are also taught a swan could break your arm if you get too close. I don't know if it's true or not because I've been too scared to find out.
They're not going to hold you down and break it with a tire iron .. but I'll bet for certain that Swans are responsible for arms being broken.
They've got a pretty savage and scary charge to them, it's highly likely they've startled more than one person in a park who've turned to run, tripped and fallen across steps or rockery edges and come out badly injured.
They are also able to swing their wings quite rapidly while charging you. In this way they can throw a surprisingly hard punch. But not break bones in healthy humans - kids included.
Black Swans in Perth, herdsman Lake and elsewhere, in the 1980s during breeding season (and likely still today) fully charged people and had the mass to knock over more than one kid or small teenager .. and scare the bejeebus out of many adults.
As I said, and supported by your link, I can't see a swan directly breaking a human bone - but they sure as hell can knock one arse over by charging and causing a step back fall over. That'll do some damge in some cases, easy.
I've never been charged by a swan, but I have been knocked into a ditch by the slightly smaller but no less aggressive Canada Goose while biking. No broken bones, but I did have to straighten the alignment of the wheels on my bike.
The smell test here is that swans are flying birds and a human is large(-ish) land mammal. Nature just cannot make a flying bird's bones strong enough because they have to be much lighter.
If we play conkers with each other's bones the swan will lose.
Was bitten by a swan as a child. Painful by all accounts, but not enough for me to remember the pain, though I recall being more careful around swans afterward Probably more scary for my parents.
