She needs to brush up on her law. Powell v. McCormack. Congress can't just refuse to seat members and the speaker especially can't. There would need to be a specific ineligibility (e.g. age). Earl Warren wrote the opinion of a 7-1 court. The dissent was only because there was an argument that the case was moot as the Representative had already been seated.
Edit: Actually, the more I look into it the more interesting the argument is as the issue is a contested election and not just a refusal to seat a member for some other reason. I'll look into this more.
From the clip it sounded like Pelosi was saying she had the absolute right to not seat any member of the House she wanted at her option. That's patently wrong. It's actually an issue of a contested election and each chamber is granted by the Constitution the role of the judge of elections, returns, and qualifications for members of their chamber. Congress has passed the Federal Contested Elections Act setting up the process for this.
So with the proper context applied, Pelosi was right in saying she had the power to not seat the Representative until the process was completed. It was actually a pretty easy decision for Pelosi. One seat wasn't going to do much and the optics would have been terrible. If it was a crucial seat that would somehow change the balance of power, I fully expect we'd have seen a different result.
Honestly, I think this is a problematic area of the Constitution. Courts have refused to get involved with Congress' power to judge who won an election calling it a political question (court speech for "it's too messy for us to get involved"). But we're already seeing the potential for this power to be abused.
You had a New Jersey congressman earlier this year ask Pelosi to refuse to seat any GOP congressman who refused to vote to certify the election under the 14th amendment that disqualifies anyone who engages in insurrection or rebellion against the US Government disqualified from serving a federal office. You had a US Congressman in all seriousness allege that a member of Congress could be disqualified from office based on a vote they cast and words they spoke in the chamber. That's pretty wild if you think about it.
I don't like the idea of the power to determine whether to seat a member of congress or judge who won an election sitting solely in the hands of people with motivation to abuse it. I would hope if it came down to abuse the SCOTUS would overcome their fear of involvement and step in but it's not a certainty.
In any event, I would call that headline very misleading and the clip lacking context.
