I really don't know what they are 'supposed' to do- My barrel band only held the air tube not the barrel and it will stack pellets on top of each other at 30-35 yds, when I do my part on the trigger pulling. It might do better than that even but my yard limits me to the distance and in the bush I don't shoot at paper to get grouping, just at pests or unwanted critters.
Gun came with a Synth. stock that began to crack, I did not try to get a warranty replacement just flitted the bill for a wood stock and took the barrel band over to the trash can- Bye to the hunk of uselessness - Saying this because MINE broke half way off on one side as it was not a full wrap around design and it got caught on some branches
From watching the video it sure doesn't look like its at a problem with removing the air tube. Looked awfully easy and I believe it looked like it missed the shroud when Rick removed it.William
LDPYes it was strange, because every picture I have seen and all the paper work that came with the gun looks like what you described (at44) and the Bt65 is just like yours. I have not taken it off yet as there is still a front sight and now a Baxter LDC and since IT IS a full wrap there is nothing to catch a get broken offI don't miss that thing and the gun does not either , in case it matter , mine was built Feb of 2014- it's a 177 and the QE version same as OP