Yeah, my big question is whether that top answer is wrong or not. Most people here seem to claim it's wrong.
That top answer is definitely wrong. Brutus's comment that the adept power Improved Reflexes doesn't stack with Boosted Attribute: Reaction is also wrong, but I am less certain about this one. I believe they both stack, but are limited by the augmented maximum for reaction.
Reference page 101. It has 5 initiatives, each with it's own formula. Only "initiative" is affected by augmentation. I believe that it is an error that the augmentation column is blank for Matrix AR Initiative; it is contradicted by page 229 ("you use your normal initiative for AR"). It may have been corrected in the errata.