Given that it is impossible for an app to actually test for dead pixels, I'm going to say Apple is on solid ground here. Any such test would rely on a human actively observing the pixels so it wouldn't be an actual measurable diagnostic.
The situation with the App Store isn't like the situation with software that isn't sold through Apple. Given that Apple test and approves apps for basic functionality before allowing them in the App Store, letting through an App that claims to provide diagnostic information about hardware is tantamount to Apple stating that app does provide hardware diagnostic information. However, the API does not provide such information and Apple is not going to hinge their warranty payouts on some, for example, 16 year old kid's idea of what makes an accurate diagnostic tool.
Apple is imagining this conversation:
"Hello Apple? I have dead pixels on
my device. How do I know? I ran an app
that says I do. Hey! You approved the
app for the App Store so that's just
like saying it does detect dead
pixels! If it didn't you shouldn't
have accepted it!"
... and Apple's lawyer gets a new Porsch.
I ran into issues with 3rd party diagnostic software back when I was at Apple. One of the big headaches is that the 3rd party diagnostics offered no protection against false positives. Customers and Apple would spend a lot of money chasing false positives and the diagnostic provider would just shrug. It wasn't their problem and it didn't cost them any money.
Official diagnostic software has to be rigorously tested as false positives cost everyone a lot of time and money. Apple is not going to make a 3rd party tool quasi-official by adding it to the App Store.