100% correct.
I'm the guy that issues those I-94's.
Verifying an I94 can be quite tedious. I had to replace my SS card a while back. Since I'm currently on a work visa while my green card is pending, I needed to supply my I-94 to the SS office who then check with DHS. Time period was 2 months. Knowing the efficiency and the current heavy workload of Immigration, I could never see an immediate response to an I94 verification request. What are your thoughts on that matter?