I didn't say one party over the other. I said one candidate over the other within a given party's primary. Primaries by definition do not pit parties against each other.
I understood what you said. I simply said the effect was trivial. You have to pick one primary or the other to vote in , in an open primary state. Few dems will actually give up the chance to select their own candidate to (hopefully) effect the oppositions primary, and the same holds true for Republicans crossing the line to vote in the Democrat primary.
The only exceptions are rural areas where one party is so entrenched that the primaries are often defacto general elections.