Seems you are right...

http://www.nolo.com/legal-encyclopedia/estate-planning-when-you-re-married-noncitizen.html

Now I remembered that I checked about this several years ago, and decided being non-citizen OK as we do not have that much money ($1mil exemption at the time) anyway. (The last resort is to become citizen before the end of probation.)  Now the exemption is $5+Mil, permanent, thanks to Obama.