The opposition party’s response to the State of the Union address is a golden opportunity for up-and-coming and lesser-known politicians to introduce themselves to the nation and boost their political profile.

Such was the case for Katie Britt, a first-term Republican senator from Alabama who, despite being a newcomer to the national stage, has been mentioned as a possible choice to be Donald J. Trump’s running mate. But her big debut on Thursday night has been marred by intense scrutiny of an anecdote at the center of her speech, which was delivered from her kitchen in Montgomery, Ala.

The story, about a Mexican who was a victim of sex trafficking at the age of 12, came in the context of an attack on President Biden’s border policies. In impassioned tones, Ms. Britt described a girl being raped multiple times a day in dire conditions at the hands of cartels before she was able to escape.

“This is the United States of America, and it is past time, in my opinion, that we start acting like it,” Ms. Britt said. “President Biden’s border policies are a disgrace.”

As a rhetorical device, it would be hard conjure up a more powerful and resonant example. But the story was highly misleading and improperly contextualized.

The woman referenced by Ms. Britt was, in fact, never trafficked across the border, nor has she sought asylum in this country. And her harrowing experience took place between 2004 and 2008, while a Republican, George W. Bush, was in the White House and President Biden was still a senator.