Why can't Natsu generate magic from eating Flame in the Edolas Arc? In the Edolas arc, earth land wizards can't use magic because it's limited. I understand all the reasons behind that ect.

But why can't Natsu generate his own magic from eating flames? It's shown him eating the flame of a torch before they enter the cave/mine tunnel, but he still can't generate magic. It didn't explain why that was!
If natsu was able to generate magic by eating fire then they also should've still had the magic that they had stored up before going to Edolas because later they explain that mages actually don't produce their own magic they have 2 "origins" that store magic that they collect from around them. I think that similar to a vacuum the atmosphere in Edolas sucked the magic they had stored out of their origins and any magic he got from eating the fire would be as well and since there is no magic around their origins can't collect magic. This is all speculation mind you none of this is in the manga or anime as far as i know as an explanation for the Edolas arc's magic use however if this is the reason then the pills would act as a way to hold magic i think. like a lacrima