It's not about a win / loss situation, but rather the point spread. Gamblers will bet against that point spread, and not the win or loss.
The gnomes of Las Vegas aren't going to dare risk putting out a line unless they have a pretty good idea about a specific game's situation. Otherwise, they'd easily open themselves up to losing shitloads of money, and that's not going to make the gambling bosses (legitimate ones or otherwise) happy at all. Heads tend to roll when that occurs, and I suspect that statement is both figuratively and literally...
Yes, a single player can certainly change the line.
I remember the 1995 Fiesta Bowl's line, where Colorado was certainly favored over our mismatched 1994 squad. Once they announced that Bobby Taylor, our best defensive player, was suspended for that game, the line tilted even more in Colorado's favor about two or three points, if I recall correctly.