This suggestion comes from http://bittorrent.org/bittorrentecon.pdf, and I think the important part is that a client should avoid downloading pieces serially one by one. When downloading serially, there’d be idle time in between requesting a piece and waiting to receive it.
This isn’t a problem as long as you’ve got multiple requests in parallel (so you aren’t “idle” at any point of time), and that would work regardless of whether you’re talking to the same peer or multiple ones - just that they need to have the required pieces available.