That's correct, and you can always go the gate before you board the plane, ask BR directly to make sure your bags were all loaded into the plane. (some airlines will voluntary ask for your baggage claim check to call and check when you have tight connection, but I guess BR didn't)

Like I said, BR is handled by possibly KA at HKG, but it doesn't really matter, they are still liable to make sure all the bags are there, it always have a 3rd party staff standing by the belt watching all the bags come out (same with NH, and earlier this year, when my bag show up at the belt at HKG with the handle damage to the point fell off completely, I showed that to the 3rd party staff, they took a photo as proof of damage, and paid me in cash on the spot as they don't replace the luggage like in the US). Since you left without file the claim on the spot, no one witness that happen other than yourself, you don't have a case with them anymore (not to mention you got your bags now, it is not like your bags were still lost), as it will all about you said he said she said, and throwing the ball at each other, BR blame UA, then UA blame BR, and it is also your decision to spend $150 to buy new clothes rather than they actually gave you that limit.

You can still write to BR to see what they say, but don't put too much high hope on the $150 you spent. If you will receive any comp at all, expect it will be some time as you probably have to send or fax the boarding pass and luggage claim check tags back to BR to review the case.