Triple Citizen
Registered Users (C)
Consuls spend 45 to 60 seconds on average on a submitted DS-156. In my personal opinion, your H-1B documents (or lack thereof) were not the reason for the denial. The consul looked at the DS-156s and determined that your parents are potential immigrants.
Thats right, the letter says that it was denied under section 214(b), for not presenting enough ties to the home country or evidence that they will come back after the trip.