See, as long as neither parent has the hidden ability, it can't be received by the offspring. That's what I mean here. The chances of getting a shiny are increased, and it's impossible to get one with a Hidden Ability.
Through SOS chaining, the odds of getting a Hidden Ability Igglybuff are increased as time moves on. By the time he gets a shiny, there's a good chance it could be a hidden ability.