I was under the assumption that if you stayed at the Boardwalk Villas you could also use the Beach Club, Even the Disney Video mentions it. am I wrong?
Yep, you are incorrect. Since the BCV opened around 2001/2002, DVC suspended pool hopping to any YC/BC/BCV pool by members. So that not only includes SAB, but also the quiet (leisure) pools at those resorts. Plus the pool at AKL is also off limits to DVC pool hopping.
In order to pool hop, you must be a DVC member staying at a DVC Resort on points. If you are paying cash, you technically are not entitled to this. If you are staying on points at a non-DVC resort, you are not entitled to this. If you are staying in a resort off site, you are not entitled to this benefit. If you are renting a reservation from a DVC member (using points and staying at a DVC resort) you are not entitled to this perk.
And, finally, if you are visiting (staying at a DVC resort on points) around any of the several blacked out periods (usually around holiday or other busy times), you can't pool hop.
Oops, one more, if the pool you want to pool hop to is busy, you can be asked to leave, even with that room ID to a DVC resort that says DVC member.