Everyone reappears by that point. Your 'rival' practically makes inter-regional trips just to end up in similar caves.
Still, though, Clair introduces herself as the 'world's best dragon master,' categorically. Given Lance, it's not entirely clear why she would be drawn to say that. Perhaps the dragon fumes from the Dragon's Den went to her head. They do seem a bit inconsistent, generally, though. After they lose, they're not sure if they won't admit the result, whether they're just monitoring your progress in the Pokémon League for some reason - apparently beating them is no longer enough to challenge that -, or whether for some reason they want to make sure that you're a dragon trainer before moving on, because apparently only Dragon-type users are allowed to go any further. That whole section seems a bit half-hearted, and perhaps was before all of the details of Lance as Champion in the League were confirmed, etc. In addition, for some reason they became incapable of making female Gym leaders who could just give you the badge without sending you on some sort of tangential errand for it, or just crying. Seemingly the Johto League is a bit lax about everything.