So even if the offensive player , by her act of interfering, prevents an sure double play, the defensive team has no recourse? Is there no way to award a second out on an interference play?

Yes, if in the judgment of the umpire, the interference prevented an obvious double play, a second out can be assessed, but the defense does not get the opportunity to make that second out themselves.

Example, from the Fed case book:

2.32 SITUATION A: B2 hits a grounder to F6. Just as F6 starts to throw to first base, R1 on the way to third base, yells at F6, which startles F6, causing the ball to be thrown over F3's head into dead-ball territory. RULING: R1 is called out immediately for interference. The ball is declared dead. If this interference, in the judgment of the umpire, is an obvious attempt to prevent a double play and it occurs before R1 is put out, the immediate succeeding runner, B2, shall also be called out. (8-6-10d)

It is also based on consistency, a BR is BR no matter why, and the ball is live except HBP.