Since $P(E|F) = \dfrac{P(E \cap F)}{P(F)}$, the condition becomes: $P(E)P(F) = P(E \cap F)$, which is exactly the definition of independence of $E$ and $F$. 

Now check each option:

1) "E and F are independent" → This is exactly equivalent to $P(E)=P(E|F)$ (TRUE). 

 3) $P(F) = P(F|E)$ → Also true under independence (TRUE). 

 4) $E^c$ and $F$ are independent → Independence is preserved under complements (TRUE). 

 2) $2P(E^c)P(F^c) \ne P(E \cap F^c)$ → This statement has no relation to $P(E)=P(E|F)$ and does NOT follow from independence (NOT equivalent). 

Therefore, the option that is NOT equivalent is: Option 2.