No. A Nalgene is one method as it gives you a positive connection, but it isn't necessary. You can backflush with narrow mouth bottles including Platypus, traditional soda plastic bottles, etc. The lid will work with Dromlite bags, Drom bags, and any other bottle that will fit a 64mm lid.

According to the official Backflushing directions included with the pump, it's recommended that you use one of three types of containers. These are:
-Hard Bottle (i.e. Nalgene, GSI, etc.)
-Flexible Water Container (i.e. Dromedary with Quick Connect Lid (comes with the HyperFlow), Dromlite, Hydromedary).
-Personal Hydration System (i.e. Platypus Big Zip, CamelBak, etc.). With these you attach the hose (removing the bite valve first) to the nipple on the end of the HyperFlow's filter head.

It's best if you can get a good seal which won't allow air into the system. Air seems to be the biggest issue when backflushing (causes it to not suck water in). A plastic soda bottle will leak, meaning you might get wet, but it should work if inverted.