I think you're being a little too liberal with the verb 'designed'. While I would lean towards J-20 being optimized toward air-2-air combat, I don't see any evidence to conclude it is designed with no ability to carry out air-2-ground strikes.
The size of its internal bays may not allow for large weapons, but given its stealth it does not need to fire from the same stand-off range as legacy fighters. Thus a smaller, shorter range weapon should be just as effective. I think something in the class of IR/TV guided Popeye II should synergize quite well with its sensor systems.
I don't think he's being too liberal with that word at all -- the phrase "designed as a strike fighter" does convey a suggestion that an aircraft was optimized for the strike role as its primary mission.
Saying that the chance of J-20 being designed as a strike fighter as "just about zero" is quite correct because it isn't a strike fighter.
However, what Iron Man said is also very consistent with the idea that J-20 is capable of conducting some strike roles. That is the difference between an aircraft "designed" to be a strike aircraft vs a multirole or air superiority aircraft with secondary strike capabilities.