Forum:Missing the timing- infernity archfiend

Hi this is my first time putting a query so do forgive me for the layout.

So the qn here is about Infernity Archfiend missing the timing to activate its effect.

On board: Me: no cards. Opponent: one set spell/trap, no hand cards

Turn XX: i activate heavy storm to destroy all spell and trap cards on the field. Opponent activates Call of the haunted to target his Infernity Archfiend (http://yugioh.wikia.com/wiki/Infernity_Archfiend) in the graveyard and special summon it. He then proceeds to search an 'Infernity" card from his deck as Infernity Archfiend was special summoned when he has no cards in hand.

Chain Link 1: Heavy Storm Chain Link 2 : Call of the Haunted

So i have knowledge about cards missing their timing to activate their effects:http://yugioh.wikia.com/wiki/Missing_the_Timing. I told my opponent that he will miss the timing to activate Infernity Archfiend's effect to search for an 'Infernity' card because the last thing in the chain is that all spell and traps on the field is destroyed (by Heavy Storm) he argues otherwise that the cards resolve individually with 'Infernity Archfiend' special summoned when he has no hand cards, he can search.

Guys, am i wrong here? Also, my opponent was a huge dick so he states that citing a single source (yugioh wikia) is not comprehensive. Do you guys have other links that can reinforce this argument if it is indeed correct?