Gibbs energy and Entropy
Reason 1: 

while $T\,\mathrm dS=\mathrm dQ$ for a reversible process, this does not mean $T\Delta S = Q$

Reason 2: 

The term "reversible reaction" is unrelated to "reversible process".

Lame Reason 3:

Because your "always" statement does not repeat the "constant pressure" requirement assumed for $Q=\Delta H$