Stats are obviously important, but I'm not sure they can ever replicate simply watching film. For instance, two weeks ago, Odell Beckham Jr of the NY Giants caught 5 catches for 44 yds and a TD. What the stat line doesn't tell you is that he actually smoked his defender a few times, was open in the endzone on a play, and if Eli had chucked it up to him or seen him in the endzone, ODB would have definitely had a couple more TDs, at least.
I don't know enough about fantasy basketball/baseball to say whether film is as powerful for those sports, but it seems like the best fantasy football analysts give heavy credence to film because it protects against overreacting to good/bad performances.
Another example - last year there was some player that saw a significant drop in touchdowns (I can't remember off the top of my head who it was). But after looking at film, it became apparent this player unfortunately kept getting tackled at the 1 yard line. Clearly, an anomaly.