FWIW I am sitting in TG lounge at BKK having just witnessed one lady and her dog checking in for UA838 - the return flight to NRT.
It's 6am here - I just took a shower - thanksgiving I am upstairs in C!!
I saw no sign of a crate or any problem with her check-in (although I wasn't immediately adjacent to her) so it looks like she has no problem to repeat the outbound trip.
Hope the dog doesn't think the same way......