I thought that's an American thing.
I don't know if it's "an American thing" but, as a resident of the USA, I find it "a stupid thing". Note my period outside the quotes.
Periods go inside quotes, in my world at least, when the quoted text originally included either a comma or period at the point where the quotation ends. Otherwise, the period goes outside the quotes, because putting it inside the quotes makes it an inaccurate quote.
Damned journalistic typesetters are idiots.
Yup. I haven't seen it in Europe, and I also find it stupid.