Sure, we'll go with that. It's better than the main reason, which was 'Strange got distracted' and 'Ignatius tried to metaphorically dangle the Mirror in front of him.' Birds can't bite their lips, but there's an odd little hesitation before Strange answers like he's biting his lip and mulling things over.

"I doubt he'd tell me even if I pushed. After all, why would he give up perfectly good information for free without getting something for himself?"

In Strange's mind, Ignatius is pretty desperate for any sort of leverage at the moment.