Stats are great to learn about players that you don't get a chance to see play, and with 700 major leaguers and thousands of minor leaguers it would be impossible to have enough scouts to get adequate coverage.
I would doubt that a major league team spends 70% on their stats function and 20% on scouting. It is probably the reverse.
What the statheads are not taking into consideration is that the stats themselves are not automatically produced. There are people who are watching these games who are recording the information. It is a form of personal scouting using statistics. Statistical reports don't include the nuances and subtleties that a scouting report will provide. The individual scouting report is always more complete if the scout has been following the player for a while.
I would liken the issue of scouting reports vs stats to internet communication vs. in-person conversations. There is a lot of internet communication today and a ton of information, but in-person communication is superior as expression, inflection and body language cannot be conveyed on the internet. Communications experts say that the nonverbal aspects of communication make a substantially larger impact than the words used to communicate.
The other thing that the statheads don't understand is that those of us who trust our eyes when we watch players day in and day out, we still look at stats, but I don't look at them to tell me how the Red Sox are performing. Occasionally, I will check the stats to get some specific information. If Pedroia is raking, I might check the stats to see what he has done in the last few weeks. The stats give me the specific information, but they merely confirm what I already knew -- that he is raking. I will study the stats of visiting players, because I don't watch them everyday. I' ll check their splits etc. Most of the time if the guy is a veteran, his stats line up with my opinion of him, but there are many times that the stats reveal that he is in an anomolous hot streak or cold streak, but as you said past performance is no guarantee of future performance. That is especially true of a player's hot streak or slump. That situation can reverse itself in a single AB, and no stat can accurately predict when. Live scouting is much more accurate in that regard as they can judge body language that indicates increased confidence, a change in the player's swing or approach etc.
In any event, this is a stupid argument. We all enjoy the game in different ways. If someone is intent on proving that he knows more about baseball than I do based on the way that I process the game, let them think so. That's their issue, not mine.