The iOS guidelines are 40 points for a button on all devices. So a button on an iPad mini is the same physical size as a button on an iPhone. Complaints about fixed finger sizes don't really make sense to me. If buttons on the iPad mini are too small, so are the buttons on every iPhone app made since 2007.
Some sites have device-specific designs, and so they present different designs for the iPad 2 and iPhone. Your comment would be applicable if the iPad Mini were indistinguishable from the iPhone and were served designs meant for the iPhone as they have roughly the same pixel density, but as it stands it is indistinguishable from the iPad 2 and thus it would be served a design not meant for its pixel density.
If you're concerned about the size of touch targets on the iPad mini, they are already the EXACT same size as the touch targets on an iPhone since the two share the same pixel density and recommended touch target size (40px).
Re-read my comment. If someone has an iPad 2 specific design which uses buttons which are 40 points wide on an iPad 2, those buttons will be less than 40 points wide when that design is inevitably served to an iPad Mini user.
If iPad Minis are served iPhone-specific designs, then you're right—it doesn't matter. And perhaps the solution is "you shouldn't be making iPad 2/iPhone-specific designs," but that's not what I'm getting at.
It is the exact same size as buttons on the iPhone if you are rendering the iPad 2 design on the iPhone as well, but in that case the button on the iPhone would be less than 40 points wide and also too small by Apple's guidelines. I am saying that it would be against Apple's guidelines on both the iPhone and the iPad 2.
That's why I mentioned an iPhone-specific design, as well. The iPhone's pixel density isn't a problem because it can be distinguished from the iPad 2. And, as you've shown, if the iPhone-specific design is displayed on the iPad Mini then there is no problem at all. The issue is that there is no way to distinguish between the iPad 2 and the iPad Mini.
These people can presumably adjust their designs so they work on the iPad mini and the new design will still work well on the iPad 2 (just with slightly roomier touch targets and slightly larger fonts).
Can someone give me a real world example of a site than needs to have separate versions for the iPad Mini and the iPad 2 where some genuine benefit accrues (ideally to the user rather than the organisation who run the site)?
I'm genuinely interested in what that site might be and what the problem with a single version which works for both devices is. At the moment all I'm hearing is a lot of vague hypotheticals and frustration but not much in the way of real reasons why it's a problem.
Are they also coding individually for every single Android device? And if so how many designers are they employing and how the hell are they justifying the expense?