Confirmed a hunch this evening. Contrary to what Google Translate will tell you, あけましておめでとうございます does not mean Happy New Year. The English expression is forward-looking ("have a good one"), but the Japanese looks backward ("glad you crossed the line safely"), and so is not appropriate when addressing someone who has lost a close relative.
It's a small point, but a reminder that machine-learning translation systems are basically just sophisticated pattern-matching engines.