Great post here by Michael Lopez, who does advanced stats for the NFL, looking at the NGS expected rush yards metric. Can we show that there actually is a difference between different running backs? The answer seems to be yes. First of all, a high performance in expected rush yards over average does a good job of predicting future workload: coaches do seem to want to give the ball to backs who perform better even after accounting for scheme and blocking. Second, random selections of carries still show correlation in expected rush yards over average.
Of course, the phrase "running backs don't matter" is a bit more complex than that. They may matter, but what if they don't matter much? The amount that running backs matter (compared to players at other positions) is also connected to a) the value of rushing as opposed to passing; b) the difference between a good running back and an average one, compared to other positions; and c) how often the most expensive running backs (in terms of draft capital or salary) turn out to actually be the better running backs, compared to other positions.