Actually, many HD channels are broadcast in 1080i@50fps like Discovery, NGC, Sony Six, Star HD 1/2.
Broadcasting in progressive would take double bandwidth of interlaced signal I guess. So its possible that the 4k signal would be interlaced too.
The channels are providing content in 1080i probably but i am telling from my experience of Airtel Digital HD. The signal output from it is detected as 720p only on my Sony Full HD 40 incher.