Correct. People come to the CS forums freaked out about it sometimes. They ask what to do and are told to report/delete the email. Don’t take the gold (bait). It might be an honest accident where someone mixed up a char name when sending gold to their alt, but maybe it is not. Either way you would want to return/report/delete.
Blizzard can trace the gold. This thread is a good example of someone caught up in illicit gold from a GDKP who got penalized. And it was upheld. It also resulted in a lot of back and forth bickering about how Blizz knows, and if it is fair to penalize someone if they were not the original gold buyer.