I think it's common military training in a lot of places. I'm italian, my dad did his service in the Engineering corps (Genio) and he told me the same story. No lock step while crossing bridges.

Never had it in re bridges, but "no lock-step while carrying a stretcher" was a mandatory part for me.

My father was an officer in the Marine Corp during WW2 and he told me (many years ago) about being taught this in his training.

It's true. My dad was a Colonel, my mum a Captain and I was a cadet! Grandad was a Major etc etc