Random, but looking at Phil Garner's Wikipedia page, his 2005 Houston Astros (who would go onto make the World Series) lost 30 of their first 45 games.
Maybe all hope isn't lost yet? Lol
The thought process may be that bringing him back out risks his availability for today.
Even so, it's better to risk that than to turn to Barnes there... 4-0 isn't a save situation, but going to Barnes seems more like a 6+ run lead kinda move