Bragging is not restricted to Americans.
Look at AN on a regular basis, any thread is launching pad for bragging.
Honestly, threads asking "What do you eat for breakfast" end up with international bragging competitions.
Any excuse to brag about anything from income, to intelligence, to moral superiority, to manly prowess in physical combat (that's fighting), to correct use of the English language...
No doubt you can think of others.
I'm not saying Americans don't brag, just that they are not necessarily the leaders in that field.