Isn't it an Indian perception that B'wood Khans have soft corner for Pakistan to the extent of actually loving the country, that they(Khans) had bloodlines related to Pakistan with ancestors from this part of the world. Not just Khans but the whole Kapoor family got descent lineage from this part of the world.
And if you take Bollywood as a separate entity, India has this 'no love lost' for Pakistan. It is more about Indians thinking of the Khans as Pakistanis than it is about Pakistanis wishing them to be Pakistanis...
Human sentiments are a complex thing, nothing constant about it, hence this perception and some reality about it.
I personally think Amir is a Pakistani trapped in India.
Cheers, Doc