If so, the pilot would have done better to keep his mouth shut. Why the hell would someone say that to a bunch of passengers who are presumably totally untrained in aviation?
The pilots are in the same plane as you. They aren’t going to just let the plane run out of fuel because some person on the ground says “sorry, can’t land at this airport yet, hang out for awhile”.
If there was a real emergency they’d be putting the plane down on the nearest runway-shaped surface no matter what.
Further, I’d wager the pilot said something along the lines of “we have twenty minutes of fuel before we need to consider diverting to [alternate airport]” or something to that effect.
Maybe pilot wanted to say what there is still enough time for them to keep waiting, but in that situation didn't though how that phrase would sound for the passengers.