The guy said "single static rectangular texture". Even if rendered at 1000fps, does this need any memory bandwidth past the initial rendering?
Uh, yes. First you need to read from texture memory and into the GPU itself during rasterization. The GPU is also writing to the front buffer. Then, after the buffers are flipped, the (now) back buffer has to be encoded and sent to your monitor. So at a very minimum you have thousands of writes and even more reads for just that one rectangle.
I think you're getting memory bandwidth confused with DMA bandwidth on your PCI-E bus. Not the same thing.