I have read a lot of different things over the years. The results of these studies are pretty varied as far as what they found to be relevant or not. If there were more consistency of these metrics translating into success, that would be one thing. But there isn't and everyone uses different methodologies to determine what is relevant or not.
I did find 
this study a year ago which I found to be pretty interesting and I like the methodology behind cross referencing combine data with approximate value data from PFR, which I think AV does a really nice job of identifying a players performance relative to their peers and even across positions.
From the study you will see that the correlation between combine metrics for all positions, the 40 yard dash is the most predictive metric across all positions.
For RB the metrics that are more relevant for players at the RB position are 40 time, weight and the 3 cone drill. None of the other metrics were considered to be relevant for the RB position.
Based on my own personal observations about the combine and the draft, I have had some success with using the 3 cone drill as a guide for players who have quick change of direction skills, which is very important for a RB to have. The drill also favors players who can use lower pad level technique to help them execute the drill more quickly. This is another important skill for a RB to have. Paying attention to the drill (which is actually more relevant for defensive end players than RB) has helped me identify some good under the radar players at times and also to avoid some other players who also did not look to have good change of direction abilities when I watch them play.
That said there have been RB with really bad 3 cone times who have been very successful NFL RB. So it isn't a hard/fast rule at all. There are too many exceptions to put too much stock in any particular drill result. There have also been some RB that people might consider to be relatively slow who have been successful at the RB as well. The metrics do not tell the whole story.
The NFL is likely better at using this information in their decision making process than we are. They have more resources committed to it and have been doing it longer as well. They pretty much all say that the metrics are only used to compare traits that are seen of the player in games. So if a measurement does not match what the player does on the field, that is cause for more investigation I think, but whatever the player timed that particular day is just one piece of a much larger puzzle.
Once the NFL drafts these guys I think you should put anything combine related aside. Because that data is already baked into the draft position.
If you look at the second to last graph in the article above, you see that NFL draft position is about twice as predictive as the combine measurements in the model across the board.