You write: "All of them come from Arabic (not just the letters, the scripts) as well, and as an Arabic speaker I find that attitude strange. I could be reading too much into it."
I think that's where our disconnect lies and I do think you're reading too much into it. Urdu is not a child of Arabic. The word itself is Turkish, and the old story about Urdu's genesis is that it amalgamated during the military conquests of Babar, a Central Asian Turk who was funded by the Ottomans but operated independently. A great percentage of Urdu was Turkish (I once heard upto 40% of the words are Turkish), and it contains many Sanskrit words as well. This notion that Urdu is a "Muslim" language, and because of that, it has some special relationship or descent from Arabic, is more of a 20th century phenomenon having to do with Pakistan's affiliation with the Arab world as a result of becoming an Islamic Republic. That's what I think. You are welcome to try and persuade me that Urdu is some kind of Arabic-lite. But in my experience except for a very small minority of very recently Arabized Pakistanis, I have never heard of that view. What I have seen more frequently, however, is resentment against the idea that Urdu is Arabic's baby. Its kind of like how the Anglicans would resent being declared Children of Catholicism. Sure, without revolting against the Church there would not Anglicanism, but that doesn't mean that an Anglican would like to be told, "you came from Catholicism."
I will give you an example. I once had an Arab yell at me for pronouncing Eteraz with a zay ending. He tried to show me that since in Arabic Eteraz ends with a dawd, and since a dawd is a hard sound, I should pronounce it Eterawd. I gently reminded him that for me it comes from Urdu and Persian and I will pronounce it with a Z. That may irk an Arabic purist. But only if he thinks that all languages written in Arabic-script should follow Arabic's rules, which makes no sense. By that logic, Indians should demand that all people who count with a zero in their system should pronounce their numbers in Sanskrit.
I did not intend to write this much in response to that one sentence, but your point of view is something I've experienced frequently enough that I felt inclined to respond longer. It is not just Arabs who say things like this, too. As I mentioned it now includes Pakistanis themselves, who consider themselves "of Arab culture." An example of these Pakistanis are kids in Lahore, Pakistan, who have a license plate tag that reads, "al-Bakistan." They want to Arabize. In you they would have an ally, I imagine :).
I appreciate you looking into my other work. If you get a chance to check out the short story collection, you will find a pre-Islamic story set in Mecca there. There is also a story set in an imaginary state called Islamistan, and there I adhere to Arabic rules of transliteration instead of Urdu or Persian i.e. Dhulfaqar instead of Zulfikar, etc.