This is not true. The equivalence point is where the formal concentration of HA (strong acid) equals the formal concentration of BOH- (strong base) added. They also react completely (neutralize) to produce a neutral solution. At the equivalence point, you basically have just H2O. pH = 7 is correct, but pKa = 7?? What species' pKa is 7 here? Certainly not water, the strong acid (pKa < -2), the protonated strong base (pKa > 16), or H3O+ (pKa ≈ -2).
At the half equivalence point [HA] = [A-] is still true, although [HA] is really [H3O+], because a defining characteristic of a strong acid is that it is stronger than the hydronium ion, which is the strongest acid that can exist in an aqueous solution. Whether you believe it or not, there is still greatest buffering in this region, it's just that the pH is usually so low that it is of no practical use. You also can't use the HH equation.