Note that 256 megs is how much physical RAM the iPad 1 has; the amount available to the foreground application is much less than that. Indeed, on the iPad 1 you're lucky if you have much more than 100 Megs to yourself while you're running.
And, as others have said, higher color depths will make some difference, and no doubt the port puts a lot less effort into RAM conservation than the original did.
All your points are correct, but when the original version required 16 MB of RAM it wasn't expected to be able to dedicate all of that to itself either.
Per one of the devs on Twitter, a lot of the difference in base memory requirement is that the original expected to have a significant swap file to work with on top of those 16 megs, while the iPad app has no such luxury.
I believe the default was 640x480x16 bit. I am not sure whether you could up it to 32 bit 1024x768 but I know you could in BGII. Still have my disks somewhere.
And, as others have said, higher color depths will make some difference, and no doubt the port puts a lot less effort into RAM conservation than the original did.