I think the ineligibility applies only to the team that is pre or post bowling. The assumption is made that if you're bowling unopposed on your regular night with other teams from the league on either side of you, you won't be tempted to cheat.
As much as my wife says that I'm more interested in beating my teammates than the other team, I hate bowling against blind scores, ghost teams and teams that are pre or post bowling. It took me twenty years to figure out that I could put my team's averages in as blind scores for the other team, and since then we've done much better against ghost teams, but its still not as much fun as bowling against real people.
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