The container (sorry; not sure what to call it) has to travel in the freight section, doesn't it? Where else could it be on a passenger plane? I'm surprised it doesn't have a flag affixed to it - I thought they all did during transport. Maybe the source is exaggerating this.
As above, if in a commercial aircraft, the flag in placed on the coffin as soon as it is unloaded.
I highly doubt a flag is affixed in transport.