This is correct. I believe the reason why they are not added to the chests is because they are tied to DLC and therefore cannot be added to the loot pool.
In V1, we had a dice table with loot and the ONLY way to get DLC weapons was to play that particular DLC map. In other words, if you wanted to get the Falchion or the Warpick, you had to play Karak Azgaraz and pray for that weapon to not only be on the table but that you rolled the correct number to get that weapon.
In V2, we get the blueprints allowing us to remove the RNG from obtaining that weapon and craft it ourselves. This is definitely way better as it took me AGES to get the Executioner Sword from replaying The Courier over and over.
In other words, it’s probably not possible for the DLC weapons to be added to the mission reward chests since they are tied to the DLC each person has to buy in order to obtain them.
I’m sure if there was a way to add DLC weapons to the normal loot pool without breaking the game for those who don’t own the DLC, Fatshark would have done it. I think it’s just not feasibly possible considering how DLC weapons were also handled in the original vermintide.
FYI, it took me 37 runs on The Courier to get a green Executioner Sword and another 19 to get the red one from a perfect roll. There is no red weapon crafting in V1 so you actually had to play Nightmare and Cataclysm.