All firefighter candidates must pass the CPAT test. It's basically an obstacle course while carrying weights and wearing a weighted vest made up of activities meant to simulate the physical needs of the job. The parameters and criteria are the same for all candidates. Here is the test requirement described for Los Angeles.
https://personnel.lacity.gov/exams/FirefighterCPATInformation.pdf
For the record, I was somewhat surprised. I expected to see different weights or time requirements for women.
Would candidates who pass this test be able to "carry" an adult person out...probably not. The corresponding portion of the test is called "Rescue Drag." I spent a little time at the firehouse and firemen when I was a kid in the 70s. (My friend's dad was assistant chief and later chief.) they were not particularly muscular strapping men. Actually pretty average. The number of them (all male at the time) who could have carried 200 pound adult me out of a burning building probably approached zero. More likely they could assist conscious me or drag unconscious me out (like in the test), but not carry.
I'm pretty sure the female firefighters I've met could do so just as well, having passed and met the same physical requirements.
As for the video of the assistant fire chief, I'd like to see what the context was and what she said next in the original video. Obviously, it came from somewhere, but I can't find any reference to an original video or what it was recorded for.