If Spain do go on to win another European Championship or World Cup, with him being a key player and knowing his penchant for hugely important contributions, to think it's completely unfathomable that he could go down as a better player than Zidane is a bit silly, IMO. He's without question one of Spain's three most influential players, I'd say he's definitely top two, and if he helps them go on to dominate the international stage in a way that not even the great Brazil team(s) did, then of course he'll have a claim as being one of the best midfielders to play the game just like Zidane. I don't think he will be considered better in the end but it's wrong to completely rule it out, IMO.
He was a genius, he is a great...there's no denying this. Part of me thought that the legend of Zidane had become so big because a) he finished his career on such a high note, headbutting aside b) he's one of the few recent greats, so many people of the recent generation feel like he's their great and thus hype him up even more and c) he had so many highlight career moments in the bigger games, and so many lower points in the smaller ones that much fewer watched. So yeah, I actually agree with the chief that Zidane will probably be remembered more fondly simply because of those highlight moments that he specialised in.
When France won the World Cup in '98 it was Zizou who won it for them, that's the lasting memory, while when Spain won in 2010 it was because they assembled one of the greatest international sides of all-time, not because Iniesta won it for them. Despite Thuram winning their player of the tournament, it's still seen as one of the defining moments of Zidane's career. Iniesta just seen as someone who played his part in a great team. I'd argue Iniesta was roughly as good in 2010 as Zidane was in 1998.