Originally Posted by
Aldoman
Is your B1/B2 visa valid for multiple entries? if so, what you're doing is something pretty common. I'm Mexican so I have a B1/B2/BCC and 90% of my TATL or TPAC flights go through the US, if you're honestly just transiting before your vacation you should have no problem
I agree. If the OP's visa is multiple entry and valid for the times to enter the U.S. and the purpose is for vacation, the vast majority of time people in this situation have no problems. Have the tickets available should the officer wish to see them.
In the OP's original quote from the CBP website, their additional concern is someone who only goes to a contiguous territory, and this is not the case for the OP. Officers are not there to trick you, but to identify people that may not be admissible for whatever reason. At the same time they are doing that, they also have to facilitate thousands of other legitimate travelers at busy airports like LAX each day. And it sounds like the OP would fall into this latter category.
A few airports in the US had in-transit lounges once upon a time. They were not common even before 9/11. Don't know if any are still in use or, if so, whether LAX has one.