Unfortunately, we don’t see the sideline judge (it’s behind us on the right). To me, it seems likely that the line judge confused singles and doubles lines, and thus called out when the shuttle was in – in doubles.
The umpire seemed surprised both times. Of course you can and should overrule if you see it’s in by 30cm, but if you are surprised and occupied by looking at both line judges (sitting at totally different directions), I understand one could be unsure of what happened and forgo overruling.
The service judge doesn’t sit in a great position on the opposite site of the court, so I would be hesitant to step in if I were her, especially if there were players between her and the shuttle.
The referee can follow the match and exchange or talk to the line judge. Without having a video replay of the incident and thus knowing it was in by a lot (and the line judge likely confused lines), the referee can’t do anything; the umpire correctly reported the line judge indicated Out, so what else is the referee gonna tell the players but to play on?
With video replays, the referee should exchange or talk to the line judge.