Nobody implied this.

All immigrants are expatriates, but not all expatriates are immigrants.

The term immigrant denotes someone who has left their native land permanently - that is, they never plan on moving back there. Many expatriates do plan on returning home, so calling them immigrants is inaccurate.

Please understand that anyone studying abroad, stationed overseas (either with the government or military), or working abroad is an expatriate - no matter where they're from and where they're living.

Isn't it the wrong word, though? From the US perspective (which is what's relevant here), he's not an immigrant.

Emigrant is the word you're looking for, since we're talking about the policies country towards someone who left it.

You're an emigrant if you left permanently, otherwise expatriate is still the correct term.