sutra: What is the model(Settings - General - About - Model) of the iPhone 5 16 GB bought from the Apple Online Store? is it "MD669X" for black one, and "MD670X" for white one?
I can't find anything online suggesting those are valid Apple model numbers.
You can find the model numbers via the Apple online store, by going through the motions of picking a specific iPhone 5 model (colour and capacity), as far as clicking the first "continue" button. They are:
MD297X/A black 16 GB
MD298X/A white 16 GB
MD299X/A black 32 GB
MD300X/A white 32 GB
MD662X/A black 64 GB
MD663X/A white 64 GB
The black 64 GB number matches what my invoice says, but I haven't received my iPhone 5 yet to confirm that is what it reports in About. (The /A suffix is probably missing on the About screen, but it is the same for everything.)