Sorry, but that´s flat out wrong. Professional teams keep losing exhibition games every now and then, and unless they do it in a row and by habit, nobody ever remembers after the next league or cup game.
This game has 22 games during season.
Each game has affect. The longer it is, the longer the affect is.
Scrimmages has affect but smaller.
Another example - if MAN-United would have lost to U-City during a preseason game, there would be a lot of noise as well.
Much smaller compared if that would have been in a league game, but it would create noise, and it would affect fan base.
More...
If LA would have lost
ALL their preseason games, wouldn't it affect the fan base? It sure would.
A single scrimmage game, as single league game, has less affect than a serie of games... But, as there is a single game affect, there is a single scrimmage game affect.