I don't know how you rebut a flawed paper without making its authors look bad? That would be a general-purpose argument against criticizing papers.
Actually, people should criticize flawed papers. That's how science works! When you publish scientific papers, you should expect criticism if there's something that doesn't look right.
The only way to avoid that is to get critical feedback before publishing the paper, and it's not always possible, so then the scientific debate happens in public.
The situation here is different though.. If I'm making an existence claim by demonstrating a constructive argument and then being criticized for it, the most effective response to that critique would be a second, alternative construction, not attacking the critic's argument. After all, I'm the one claiming existence.. the burden of proof is on me, not my critics.
I don't know which argument is more constructive, though? Both teams reported what they did. They got different results. Figuring out why is the next step, and pointing out that they did different things seems useful.
Though, the broader question is how useful the results of the original paper are to other people who might do the same thing.
Actually, people should criticize flawed papers. That's how science works! When you publish scientific papers, you should expect criticism if there's something that doesn't look right.
The only way to avoid that is to get critical feedback before publishing the paper, and it's not always possible, so then the scientific debate happens in public.