Joseph, "As it happens" is used to introduce a statement, usually a suprising statement. The author of the article suggests that it is suprising that the Americans must test European electric razors a second time, when it is unlikely that these razors will electrocute Americans. The safety of European razors is America is not a given because in the US electric appliances are adapted to a 120volt current, while Europe appliances use a 250volt current. If one of these razors does cause harm to a purchaser in the US, you can be sure that the company will be sued for millions of dollars. However, it is possible to make electronic products, computers for example, that can use either 120volt or 250volt currents. 'Actually' or "as a matter of fact" would be a good synonyms for "as it happens" in the context of your sentence because either of these can be used to introduce something unexpected or suprising. Example, Actually, I'm not a real doctor, although I play one on TV. I was not a poor student, as a matter of fact, I graduated first in my class.

A variant is "as it so happens..." You use it to connect the following statement to what you've just said, like an additional comment which summarises your main point(s). You could also use, "for that matter, ..."

You might say "In fact..." Another way of putting it (in a more wordy way) is "The actual truth is that..."