It's probably worth having a look at http://www.brewersfriend.com/2013/04/24/using-your-refractometer-correctly-for-maximum-accuracy-in-home-brewing/to understand the reason for their recommendations.
In that article, they state:
"Cheap refractometers are not very consistent measurement to measurement from the same wort. I take 5+ measurements then average the value before recording. The variance is +/- 10% either way! What a joke. You get what you pay for and this unit was a gift."
This would explain why they took 5 readings from each batch, and averaged the readings to get a single input to the calculator. I usually just take a single reading, and check the results from my calculator. Very occasionally, I will take another reading if my calculator shows an unexpected gravity value, or if I forget the reading before getting to the calculator. I think that his refractometer is faulty, but next time I brew I will take multiple readings and see if I can detect any difference.
I do notice that the Brix reading drops a bit if I add hot wort to the refractometer and read the results immediately, but it stabilizes as the wort cools down, and I read the results after about 1 minute (by which time the reading is stable).
As you need a hydrometer to calculate the correction factor, you should use the hydrometer for your next brew and just use the refractometer to calculate the correction factor. For subsequent brews (once the correction factor has been calculated) you can use the refractometer alone, but it's still probably worthwhile to use both instruments for a few brews to average the correction factor.