I don't believe this bag backflush method provides enough pressure to backflush and clear out the entire diameter of tubules, the syringe provided provides a huge amount more pressure, not sure if I'd recommend or use this idea, and I'm somewhat surprised nobody has mentioned this problem in this thread, you may end up creating the center channel with clogged outer channels that sawyer warns about. There's apparently a fair number of reports of filter slowdown over time, one has to wonder if methods like this are not partially to blame.
If you use an adapter and a short piece of hose and a syringe with a tip that fits into the hose, you can get far far higher pressure for backflush, simple physics, force per square cm, plunger has more force, and that's brought down the small opening.
while appealing to get rid of the syringe, I would say that this is probably not the way to do it. On the bright side, I've heard that sawyers can now be bought at walmart for $36 though of course I don't advocate buying from that place, you can probably find it online for that price too, so ruining a few filters over time isn't really going to be break the bank.