If you think about it -- this is what you're supposed to be doing throughout a chess game -- the players have been "thinking" about it for a while (whatever time control) -- setting themselves up to be able to put-up a fight, possibly game (or, gain) some time (on increment).
As
@tpr mentioned -- some people play well under time trouble.
In addition, the faster the pace ... someone not under time trouble might move faster trying to force the person in time-trouble to time-out ... and mistakes are made, which can be quickly capitalized upon, while gaining that increment. It's like an opening-trap, but for end-games.
Just to be clear, there are other measures, such as, it's commonly taught that you shouldn't study openings, and concentrate on mid-game tactics, strategy and "shots." Where a person may have a poor opening, someone who follows traditional studying suggestions may have a strong mid-game, or end-game (again, study mating patterns, end-game tactics and strategy, etc). Also consider that as time runs-out, in the end-game, there are fewer pieces to manipulate, and calculations can get easier (or, the converse: more tedious).
As a general rule, I don't play anything greater than 1-second increment. Two or Three second increments allow players to do this (flag on practically zero time) -- especially because I mostly play ZH.
If you're sitting on time, and your opponent is not, you could use that time to plan strategy or tactics. Your opponent (lacking time) is also using the time to think and plan, knowing he or she is down. Your opponent is preparing (possibly a pre-move), while you're sitting on time thinking (your opponent is using your time).
Even on a 1-second increment, if we had an enforced 1/10'th penalty on each move (instead of zero penalty since lag is compensated, and a good connection means 0-time spent on a pre-move) ... someone with zero time could easily flag someone of approximately equal rating with a full clock minute (or more). Strange things like this have been seen and complained about.