tl;dr: Do not aim to prove their way wrong; aim to find the right way instead.

Do not make yourself a remote verifier or something like that.

If you write I don't think those conclusions are remotely justified by the data. You are stating that their approach is wrong. Period. You don't need to wrap it in nice words either.

I can read from your question that You were hired to improve usage of statistical tools in your team. Do your job.

1. Try to understand.
   Ask them to explain their work to you. You all will find why they come to that conclusion, that the conclusion is wrong, why it is wrong and you can suggest different approach. Ask appropriate questions: "What does that mean..." "Why was this parameter neglected?"
2. Help them.
   Suggest different approaches and methods. Offer them your assistance with such tools.
3. Be open.
   Be ready to say that You did't get their picture or made wrong conclusion. Sometimes the deeper discussion reveals all the hidden points that were missing in the text, because they though "it is easy to see", but it isn't.

On the other hand, if you want to help them to prepare for a conference, the colder and nastier questions and notes you have he better they will be prepared for the actual questions from the audience.

tl;dr: Do not aim to prove their way wrong; aim to find the right way instead.

Do not make yourself a remote verifier or something like that.

If you write I don't think those conclusions are remotely justified by the data. You are stating that their approach is wrong. Period. You don't need to wrap it in nice words either.

I can read from your question that You were hired to improve usage of statistical tools in your team. Do your job.

1. Do not be rude.
   State your concerns and points without mocking them or using rude words tec. During chit-chat you can mention where you were wrong etc. Some people are offended when you use overpolite and defensive language - they want hard facts, not digging out them from 2hour monolgue. Some people are crushed by emotionless facts - they took their work personally. Allways try to find something right and mention it.
2. Try to understand.
   Ask them to explain their work to you. You all will find why they come to that conclusion, that the conclusion is wrong, why it is wrong and you can suggest different approach. Ask appropriate questions: "What does that mean..." "Why was this parameter neglected?"
3. Help them.
   Suggest different approaches and methods. Offer them your assistance with such tools.
4. Be open.
   Be ready to say that You did't get their picture or made wrong conclusion. Sometimes the deeper discussion reveals all the hidden points that were missing in the text, because they though "it is easy to see", but it isn't.

On the other hand, if you want to help them to prepare for a conference, the colder and nastier questions and notes you have he better they will be prepared for the actual questions from the audience.