DesertLili, you appear to have made a conclusion based on one paper you've read. There is plenty of literature on HCV and autophagy. Here is a quick rundown for you:
All successful intracellular pathogens disrupt autophagy in some way at one of its many stages (unsuccessful pathogens succumb to it right away). Most pathogens, both viruses and bacteria, jam authophagy machinery by secreting certain metabolites -- until a stronger signal overcomes it, allowing autophagy to complete and so destroy them in the process. Fasting is the strongest inducer of autophagy known.
Now, most of the pathogens succumb to this strong signal and that's why fasting, when done right, can rid the body of many chronic infections. However, there is a handful of pathogens that exploit autophagy machinery for their own replication. HCV is one such pathogen but there are others. For example, bad breath many people experience during a fast is due to metabolites of a very common bacterium, P. gingivalis -- it also exploits autophagy machinery for its growth; it flares up during a fast and quickly goes into remission upon refeeding.
Fasting is contraindicated when such pathogens are present for the simple reason that they proliferate during a fast. It is true that young, strong (and well fed before the fast) people can overcome the simplest of such infections during a fast (because the immune system has many tricks up its sleeve besides autophagy) -- but this generally does not apply to most people who turn to fasting in order to cure some chronic condition.
There is a Russian forum, golodanie.su where a number of people with HCV tried to beat it with fasts. None of them succeeded, some seriously worsened their condition to the point of appearance of the characteristic skin rush of HCV. Most claimed they felt much better after the fast, but very few of those who did the viral load test before and after had the proof that the virus flares up during a fast.
Then, also in Russia, there is a long fasting tradition supervised by MDs that spans many decades and according to it, fasting is contraindicated with viral hepatitis (this was already known before HCV was identified as such).
Based on all this theoretical and empirical knowledge, fasting beyond a few days is a serious no-no with Hep C.